Access the full text.
Sign up today, get DeepDyve free for 14 days.
Carlos Caleiro, J. Marcos, Marco Volpe (2014)
Bivalent semantics, generalized compositionality and analytic classic-like tableaux for finite-valued logicsTheor. Comput. Sci., 603
Rafael Bordini, J. Hübner, M. Wooldridge (2007)
Programming Multi-Agent Systems in AgentSpeak using Jason (Wiley Series in Agent Technology)
Anand Rao, M. Georgeff (1997)
Modeling Rational Agents within a BDI-Architecture
M. Baczyński, B. Jayaram (2008)
Fuzzy Implications, 231
B. Bedregal, A. Cruz (2008)
A Characterization of Classic-Like Fuzzy SemanticsLog. J. IGPL, 16
M. Fitting (1991)
Many-valued modal logicsFundam. Informaticae, 15
Merrie Bergmann (2008)
An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems
Christopher Peacocke, J. Searle (1986)
Intentionality: An Essay in the Philosophy of Mind.The Philosophical Review, 95
J. Nacht (2016)
Modal Logic An Introduction
M. Bratman, David Israel, M. Pollack (1988)
Plans and resource‐bounded practical reasoningComputational Intelligence, 4
G. Dimuro, A. Santos, B. Bedregal, A. Costa (2009)
Fuzzy Evaluation of Social Exchanges Between Personality-based Agents
P. Busetta, R. Ronnquist, A. Hodgson, A. Lucas (1998)
Jack intelligent agents - components for intelligent agents in java
W. Hoek, M. Wooldridge (2003)
Towards a Logic of Rational AgencyLog. J. IGPL, 11
Ana Casali, L. Godo, C. Sierra (2009)
g-BDI: A Graded Intensional Agent Model for Practical Reasoning
Proceedings of International Conference on Information Processing and Management of Uncertain in Knowledge-Based Systems
M. Winikoff, L. Padgham (2004)
The Prometheus methodology
M. d'Inverno, D. Kinny, M. Luck, M. Wooldridge (1997)
A Formal Specification of dMARS
Zaiyue Zhang, Yuefei Sui, C. Cao (2004)
Fuzzy Reasoning Based on Propositional Modal Logic
S. Parsons, O. Pettersson, A. Saffiotti, M. Wooldridge (2000)
Intention Reconsideration in Theory and Practice
Robert Lin (2014)
NOTE ON FUZZY SETSYugoslav Journal of Operations Research, 24
S. Shen, Gregory O'Hare, Rem Collier (2004)
Decision-making of BDI agents, a fuzzy approachThe Fourth International Conference onComputer and Information Technology, 2004. CIT '04.
M. d'Inverno, M. Luck (1998)
Engineering AgentSpeak(L): A Formal Computational ModelJ. Log. Comput., 8
Ana Casali, L. Godo, C. Sierra (2011)
A graded BDI agent model to represent and reason about preferencesArtif. Intell., 175
Zaiyue Zhang, Yuefei Sui, C. Cao, Guohua Wu (2006)
A formal fuzzy reasoning system and reasoning mechanism based on propositional modal logicTheor. Comput. Sci., 368
A. Cruz, B. Bedregal, R. Santiago (2014)
On the Boolean-like Law I(x, I(y, x)) = 1Int. J. Uncertain. Fuzziness Knowl. Based Syst., 22
Claudio Callejas, J. Marcos, B. Bedregal (2012)
On Some Subclasses of the Fodor-Roubens Fuzzy Bi-implication
B. Bedregal, A. Cruz (2005)
Propositional Logic as a Propositional Fuzzy Logic
(1987)
Intentions, plans and practical reason
A. Dragoni, P. Giorgini (1996)
Belief Revision Through the Belief-Function Formalism in a Multi-Agent Environment
T. Vu, P. Siebers, Christian Wagner (2013)
Comparison of crisp systems and fuzzy systems in agent-based simulation: A case study of soccer penalties2013 13th UK Workshop on Computational Intelligence (UKCI)
G. Farias, G. Dimuro, Glenda Peter, Esteban Jerez (2013)
A BDI-Fuzzy Agent Model for Exchanges of Non-economic Services Based on the Social Exchange Theory2013 Brazilian Conference on Intelligent Systems
J. Rubiera, J. Molina, J. Davila (2001)
A BDI agent architecture for reasoning about reputation2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236), 2
P. Hájek (1998)
Metamathematics of Fuzzy Logic, 4
A. Cruz, B. Bedregal, R. Santiago (2018)
On the characterizations of fuzzy implications satisfying I(x, I(y, z))=I(I(x, y), I(x, z))Int. J. Approx. Reason., 93
Adriano Dodó, J. Marcos, F. Bergamaschi (2013)
On classic-like fuzzy modal logics2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS)
Philip Cohen, H. Levesque (1987)
Intention = Choice + Commitment
Anand Rao, M. Georgeff (1993)
Intentions and Rational Commitment
C. Morgan (2003)
Two values, three values, many values, no values
Guest Editorial
North American Fuzzy Information Processing Society Annual Conference NAFIPS ’
G. Dimuro, A. Costa (2015)
Regulating social exchanges in open MAS: The problem of reciprocal conversions between POMDPs and HMMsInf. Sci., 323
S. Parsons, P. Giorgini (2000)
An approach to using degrees of belief in BDI agents
R. Santiago, B. Bedregal, A. Madeira, M. Martins (2019)
On interval dynamic logic: Introducing quasi-action latticesSci. Comput. Program., 175
J. Blee, D. Billington, Guido Governatori, A. Sattar (2008)
Levels of Modalities for BDI Logic2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, 3
M. Wooldridge (2000)
Reasoning about rational agents
X. Caicedo, R. Rodríguez (2011)
Bi-modal Gödel logic over [0, 1]-valued Kripke framesArXiv, abs/1110.2407
FUZZY INFORMATION AND ENGINEERING 2021, VOL. 13, NO. 2, 139–153 https://doi.org/10.1080/16168658.2021.1915455 a b c Anderson Cruz , André V. dos Santos , Regivan H. N. Santiago and Benjamin Bedregal Instituto Metrópole Digital – IMD, Universidade Federal do Rio Grande do Norte – UFRN, Natal, Rio Grande do Norte, Brazil; Programa de Pós-Graduação em Modelagem Computacional – PPGMC, Centro de Ciências Computacionais – C3, Universidade Federal do Rio Grande – FURG, Rio Grande, Rio Grande do Sul, Brazil; Departamento de Informática e Matemática Aplicada – DIMAP, Universidade Federal do Rio Grande do Norte – UFRN, Natal, Rio Grande do Norte, Brazil ABSTRACT KEYWORDS Agents; fuzzy logic; BDI logic; The BDI logic is an important and widely used theoretical appara- LoRA tus to represent and reason about rational agents. However, the BDI logics are incomplete regarding the intention reconsideration, override of intention, the deliberation process, and belief revision. These are essential processes of the BDI model. Also, some rational agents, especially human being, have not the approximate reason- ing well represented by the BDI logics. So, in this paper, we define fuzzy semantics for a BDI language that is capable to eliminate those limitations. Additionally, we show how this paper is related to cur- rent works about BDI agents and discuss how those limitations can be fixed through the extension of the BDI logic to a fuzzy BDI logic. 1. Introduction An agent is an entity which interacts with the resources from the environment or with other agents. The literature of multiagent systems usually classify the agents as reactive, rational (also known as cognitive, or intelligent), or hybrid agents. In this paper we focus on the rational one. The rational agents are able to acts in a deliberate manner (practical reason- ing). How it can do this is a question, whose a widely used response is Belief-Desire-Intention (BDI for short) model (see [1,2]). According to the BDI model, the practical reasoning is given by two steps: the delibera- tion process where the agent commits itself with an intention, from its own beliefs, desires and a previous intention; and the means-ends reasoning where the agent build a plan or recipe, i.e. a set of states to be achieved sequentially, to read the chosen intention. Second [3], three points contribute to the success of the BDI model: it has a philosophical foundation [1]; some BDI logics formalisations were defined [4–7] ; and some implementa- tions use the BDI approach – as examples of implementations or computational tools which have conceptual roots in the BDI model, see [9–13]. CONTACT Anderson Cruz anderson@imd.ufrn.br [4]isbasedon [8] and [1]. While [5–7] are based only on [1]. © 2021 The Author(s). Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 140 A. CRUZ ET AL. The formalisation is the best way to understand and detail the processes of the BDI model. Moreover, the formalisation assures that an implementation of a BDI reasoning agree with the philosophy behind the model. The best-known BDI logics (based only on Bratman’s Theory) are BDI Logic by Rao and Georgeff – firstly described in [5] and revisited in [6] – and LoRA (Logic of Rational Agents) by Wooldridge [7]. Those logics are incomplete regarding the deliberation and the reconsideration of beliefs and intentions (see [6,section 7]). One way to bypass such limitations is to consider the uncertainties of the agents at the moment they express their beliefs, desires and intentions. So they can deliberate or recon- sider based on the uncertainty degree of their beliefs, desires and intentions, by choosing what they are more confident of. On the other hand, the classical formal semantics is founded under the principles of bivalence, i.e. sentences are either true or false, and truth functionality which means that the truth value of logically complex sentences are given in function of the truth values of their subsentences [14]. Historically, problems that arise from these two notions when dealing with some incomparable information have motivated to discard the principle of bivalence and consider three values or, more generically, many truth values [15]. The set of these truth values can be finite as in [16] or infinite as proposed by Lotfi Zadeh when introduced the Fuzzy logic in [17]. Fuzzy logics model the uncertainty, vagueness, and ambi- guity present in the real world by mapping sentences to truth degrees of the real interval [0; 1] and by the basis for the approximate reasoning, i.e. methods and methodologies to reasoning with imprecise inputs to obtain meaningful outputs. Inference in approximate reasoning has strong and important differences with the inference in classical logic. Indeed, in the former, the consequences of a set of fuzzy propositions depend on the underlying meaning of such fuzzy propositions. Thus, inference in approximate reasoning is a compu- tation with the possible fuzzy sets which give meaning to the set of fuzzy propositions [18]. Thereby, one way to overcome the limitations of BDI is to fuzzify the BDI logic, i.e. consider a fuzzy semantics for it. Also contributed to the employment of the Approximate Reason- ing in the BDI model. The approximate reasoning becomes the BDI model more faithful to the human being reasoning representation and maintains the model capable of reasoning about simpler rational agency. According to this new fuzzy BDI model, the agent has an initial intention and some ini- tial beliefs – with possibly different degrees of truth indicating that there are some agent’s beliefs stronger than others. Based on them, the agent selects some states to reach (called states of desire) – each desire has a degree of will. From the degrees of will added to its beliefs and its previous intention, the agent decides for, and commits itself with, one of the states of desire (such committed state becomes the new agent’s intention ). In the sequence, the agent realises the means-ends reasoning. 1.1. BDI Logic The BDI logics are first-order multi-modal temporal action many-sorted logics. They are extensions of the classical first-order logic with three types of modalities: Bel, Des and Int. Beyond those modalities, there are temporalities (Table 1) and each world is defined as A fuzzy inference system can be used in this step. Depending of the calculation used in this step, intentions with different truth degrees could be inferred, but just one of them (that one which has the major degree, for example) is adopted as the agent’s intention. FUZZY INFORMATION AND ENGINEERING 141 Table 1. Temporal operators. Formula Interpretation ϕϕ is true in the next time-point ♦ϕϕ is eventually true ϕϕ is always true ϕ Uψϕ is true until ψ becomes true ϕ Wψϕ is true unless ψ is true Figure 1. Example of a world according to BDI logics. Note: Note in the Figure 1 that one time-point – t0 – is adopted to represent the time ‘now’. Table 2. [7,table 3.6] Constructions for action expressions. Formula Interpretation α; α α followed by α α|α either α or α α α repeated more than once ϕ? ϕ is satisfied a time-tree (see Figure 1). Each node (or state) of this time-tree is a time-point which are related by an arc where the actions are presented. The time-tree is discrete, bounded in the past (there is an initial time), linear in the past (there is just one past history), unbounded in the future (there is no end-time) and branching in the future (the course of future events is yet to be determined). There are constructors of actions (Table 2) and operators over actions (Table 3). The BDI logics are said to be many-sorted since it permits the quantification over agents, (sequence of) actions, groups of agents and other individuals in the world. 142 A. CRUZ ET AL. Table 3. Operators over actions. Formula Interpretation Happens(α)action α happens next Achvs(α)(ϕ)action α occurs and achieves ϕ Agts(α)(g) group g is required to do action α The state of an agent is defined by its beliefs, desires and intentions and their semantics are given using the Kripke semantics [19]. The Rao and Georgeff’s BDI Logic has a similar definition for Model. The relevant differ- ence between the semantics of the BDI logics is that BDI Logic assumes a specific relation between the mental attitudes called strong realism. Another important feature of the BDI Logic, which is not contemplated in LoRA, is that BDI Logic distinguishes a non-occurred event from a failed or successful event. Another contribution given by the authors of [5,6] is the formal definition of the widely used term sub-world. We say that w is a sub-world of w , denoted by ww ,iff every paths and valuation of formulae contained in w is also in w . In this paper, we intend to eliminate the mentioned limitations and to put the BDI model closer to the human reasoning representation by allowing agent’s beliefs, desires and inten- tions to be quantified into the interval [0,1]. Therefore, we concern to define a fuzzy BDI logic. In this section we show a generic informal semantics found in the BDI logics [5,7]and based on this informal semantics, in Section 2 we define a semantic approach of a fuzzy BDI Logic using the classic-like fuzzy semantics defined in [20] and the first family of many- valued modal logic described by Fitting in [21]. In Section 3 are shown related work the BDI agents and applications. Further, in Section 4 we discuss about other related works and ratify the importance of the fuzzy semantics in the BDI model. For more details of the BDI logics presented in this section, see [5–7]. 2. Fuzzy BDI Logic Others fuzzy (or many-valued) modal logics have already been defined (see for example [21–27]). In the approach proposed in [23,28], the propositional connectives are interpreted as t-norms, t-conorms, fuzzy implications, fuzzy negations are considered in such a way that the classical tautologies are preserved as in [20,29] and the modal connectives have a semantic similar to the proposed by Caicedo and Rodríguez [30]. In particular, the authors seek a characterisation of fuzzy connective which maintains the usual theorems of modal logic into fuzzy setting. Fitting [21], in particular, investigates two families of many-valued modal logics and the first one determines the truth value of a modal formula based on its sub-formulae values in each accessible world. This notion is extended in this paper to a fuzzy BDI semantics where the notions of t-norms, t-conorms, fuzzy negations, implication and bi-implication [18,20,31–33] to give semantic, respectively, to the propositional connectives and, ∨, ¬, →,and ↔. Read ‘iff’ as ‘if, and only if’. FUZZY INFORMATION AND ENGINEERING 143 Definition 2.1: Let T, S, J, E: [0; 1] → [0; 1] and N: [0; 1] → [0; 1] be functions. Then (1) T is a triangular norm (t-norm) if it satisfies commutativity, associativity, monotonicity and 1 acts like an identity element (1-identity). (2) S is a triangular conorm (t-conorm) if it satisfies commutativity, associativity, mono- tonicity and 0 acts like an identity element (0-identity). (3) N is a fuzzy negation if N(0) = 1, N(1) = 0and N is decreasing. (4) J is a fuzzy implication if J is decreasing with respect to the first variable, increasing with respect to the second variable and if it satisfies boundary conditions, i.e.: J(0, 0) = J (0, 1) = J (1, 1) = 1and J (1, 0) = 0. (5) E is a fuzzy bi-implications if it satisfies the following properties (1), (2) and (3). E(x,y) = E(y,x); E(0, 1) = 0; and E(x, x) =1(1) If x ≤ y ≤ z, then E(x,z) ≤ E(x,y) (2) If x ≤ y ≤ z, then E(x,z) ≤ E(y,z) (3) 2.1. BDI Syntax The BDI language is defined in three steps. In the first one we define a language for events: E E E E E L = ,G , where = ∪ is the alphabet of events and G ={E ,E ,E , Ac Construct 1 2 3 E } is the set of grammatical rules, such that: ={α , α , α , ... , β , β , β , ... , γ , γ , γ , ... } is an enumerable set of actions; Ac 1 2 3 1 2 3 1 2 3 ={;, /, ∗} is the set of constructors of actions expressions; and Construct − α, β α, β α E E E E (4) 1 2 3 4 α α; β α|β α∗ Remark 2.1: The elements of such language are called events, and they are denoted by e. The interpretation of constructors of action expressions is the same viewed in Table 2. T T T T In the second step, we define the language of terms L such that L = , G with = X ∪ ∪ ∪{(, ), , } and G ={T ,T ,T }, where C F 1 2 3 (1) X ={x ,x ,x , ... , y ,y ,y , ... , z ,z ,z , ... } is an enumerable set of symbols of 1 2 3 1 2 3 1 2 3 variables; (2) ={a ,a ,a , ... , b ,b ,b , ... , c ,c ,c , ... }is an enumerable set of symbols of C 1 2 3 1 2 3 1 2 3 constants; (3) ={f ,f ,f , ... }is an enumerable set of symbols of functions; and F 1 2 3 − − τ ,...,τ 1 n (4) T ,x ∈ X; T ,a ∈ ;T ,f ∈ and arity(f) = n. 1 2 C 3 F x a f (τ ,...,τ ) 1 n bdi bdi bdi bdi Finally, in the third step we define the BDI language L = ; G ,let be the bdi bdi E T alphabet and G the grammatical rules of the BDI language such that = L ∪ L ∪ Gr bdi ∪ ∪ L ∪ , where: R P L Gr (1) L = ∪ is a finite set composed by agents and groups of agents – an element Ag Gr Gr of L is denoted by ι. 144 A. CRUZ ET AL. (a) Ag ={ag1, ag2, ag3, ... } is an enumerable set of agents; (b) Gr ={gr1, gr2, gr3, ... } is an enumerable set of groups of agents; (2) ={P ,P ,P , ... }: : :g is an enumerable set of symbols (or first-order predicates); R 1 2 3 (3) ={(, ), ., , } is an enumerable set of symbols of punctuation marks; bdi (4) ={ and, ∨, ¬, →, ↔, ∀, ∃, ◦, ♦, , U, W,?, Inev, Opt, Bel, Des, Int, Succeeds, Fail, Does, Succeeded, Failed, Done, Agts, Achvs} is a set of logical symbols. bdi G ={F , ... , F } such that: 1 30 τ , ... , τ ϕ 1 n F1 , R ∈ ,arity(R) = n and τ ∈ L , ∀j · (1 ≤ j ≤ n) F R j 2 R(τ , ... , τ ) ¬ϕ 1 n ϕ, φ ϕ, φ F F 3 4 ϕ ∨ φ ϕ ∧ φ ϕ, φ ϕ, φ F F 5 6 ϕ → φ ϕ ↔ φ ϕ ϕ F ,x ∈XF ,x ∈ X 7 8 (∃x · ϕ) (∀x · ϕ) ϕ ϕ F F 9 10 ϕ ♦ϕ ϕ ϕ, φ F F 11 12 ϕ ϕU φ ϕ, φ ϕ,ag F F 13 14 ϕWφ Bel (ϕ) ag ϕ,ag ϕ,ag F F 15 16 Des (ϕ) Int (ϕ) ag ag ϕ ϕ F F 17 18 Inev(ϕ) Opt(ϕ) e , e e , e 1 2 1 2 F F 19 20 e ; e e |e 1 2 1 2 e ϕ F F 21 22 e∗ ϕ? ϕ,e,ag ϕ,e,ag F F 23 24 Succeeds (e[ϕ]) Fail (e[ϕ]) ag ag ϕ,e,ag ϕ,e,ag F F 25 26 Does (e[ϕ]) Succeeded (e[ϕ]) ag ag ϕ,e,ag ϕ,e,ag F F 27 28 Failed (e[ϕ]) Done (e[ϕ]) ag ag e, gr e, ϕ F F 29 30 Agts(gr, e) Achvs(e, ϕ) bdi bdi L is the language generated by the formal languageL . The brackets in the grammatical rules F –F indicate that the ϕ is optional. 23 28 The ϕ will be added in the formula iff ϕ is satisfiable after the event. FUZZY INFORMATION AND ENGINEERING 145 2.2. Fuzzy BDI Semantics bdi A BDI language supports several semantics for L . All these semantics are crisp, now will be presented a fuzzy semantics for the BDI language. Definition 2.2 shows a fuzzy seman- tic for a propositional language. Definition 2.6 presents an evaluation and Definition 2.7 presents a model M of the fuzzy BDI Logic. Definition 2.2: ([20]): A fuzzy semantic for the propositional connectives, or just a fuzzy semantics, is a tuple T = N, T, S, J, E, where N is a fuzzy negation, T is a t-norm; S is a t-conorm; J is a fuzzy implication and E is a fuzzy bi-implication. Definition 2.3: Let T = N, T, S, J, E be a fuzzy semantic and k ∈ (0, 1]. We say that T is k-crisp if for each x, y ∈ [0, 1] we have that (1) N(x) ≥ kiff x < k; (2) T(x,y) ≥ kiffx ≥ kand y ≥ k; (3) S(x,y) ≥ kiffx ≥ kory ≥ k; (4) J(x,y) ≥ kiffx < kory ≥ k; and (5) E(x,y) ≥ kiff (x ≥ kand y ≥ k) or (x < kand y < k). Definition 2.4: ([7]): A model for LoRA is a structure M = T , R, W, D, Act, Agt, B, D, I, C, L p where T is a set of all time points, R ⊆ T × T is a total backwards-linear branching time p p p relation over T , W is a set of worlds over T , D = D , D , D , D is a domain composed p p Ag Ac Gr U by a non-empty set of agents (D ), a non-empty set of actions (D ), a non-empty set of Ag Ac group of agents (D ) and a non-empty set of other individuals (D ). Act:R → D associates Gr U Ac an action with every arc in R; Agt: D → D associates an agent with every action. B, D and Ac Ag I are accessibility relations where B: D → ℘(W × T × W); D ⊆ D → ℘(W × T × W); and Ag p Ag p ¯ ¯ I: D → ℘(W × T × W). C: Const × T → D (D = D ∪ D ∪ D ∪ D ) is a function that Ag p p Ag Ac Gr U interprets constants. : Pred × T → ℘( D ) is a function that interprets predicates. p u∈N The semantics of the modalities Bel, Des and Int are defined through those accessibility relations B, D and I as follows: M , V, w, t |=Bel (ϕ) iff ∀w ∈ W, (w ∈ B (i) → M , V, w , t |= ϕ) (5) L i L M , V, w, t |=Des (ϕ) iff ∀w ∈ W, (w ∈ D (i) → M , V, w , t |= ϕ) (6) L i L M , V, w, t |=Int (ϕ) iff ∀w ∈ W, (w ∈ I (i) → M , V, w , t |= ϕ) (7) L i L t s where M is a model for LoRA, V is a variable assignment, w is a world in M and t ∈ T is a L L p time point in w. A complete definition for k-crisp fuzzy semantics could be given using partitions as in [20,23]. The variable that denotes agent is ‘i’. 146 A. CRUZ ET AL. Thus, the semantics of Bel relates a world w at a time t – called situation and denoted by w or by the pair (w, t) – to a belief-accessible world (belief-world for short) where the agent’s belief is true. D and I semantics are defined analogously. ¯ ¯ D is a subset of D for the situation w . The truth values of free variables are assigned in w t each situation by a function ρ : L → D ,suchthat: w w t t arity(f ) ¯ ¯ (1) ∀f ∈ , w (f): D → D ; F t w w t arity(P) (2) ∀P ∈ , w (P) ⊆ D ; R t (3) ∀a ∈ , w (a) ∈ D ; C t w (4) ρ (a) = w (a)foreach a ∈ ; w t C (5) ρ (x) = w (x)for each x ∈ X; w t (6) ρ (f(τ , ... , τ )) = w (f)ρ (f(τ ), ... , ρ (τ )). w 1 n t w 1 w n t t t The relation symbols are interpreted as fuzzy relations (from the fuzzy theory), the propo- sitional, modal and temporal symbols have a fuzzy semantics, but Succeeds, Fail, Does, Succeeded, Failed, Done, Agts and Achvs have not – since M has not degrees over acces- sibility relations. Those cited connectives are interpreted similarly to the same symbols in the BDI logics [5,7]. Definition 2.5: Each world is a tuple T , R , Suc , Fal where T ⊆ T is the set of time- p w w w p p w w points in the world w, R ⊆ T × T is a total backwards-linear branching time relation w p p w w Gr E over T ,and Suc , Fal : L ×R → L are functions that map agents and adjacent time- p w w w points to events such that Suc (Fal ) maps to time points that represent the successful w w (failure) occurrence of the event. The definition of sub-world is similar to [5,6,definition 6]. bdi Definition 2.6: Let T = N, T, S, J, E be a fuzzy semantic. V: S × L → [0, 1] is an evalu- bdi ation function, with respect to T , if maps well-formed formulae (wff for short) of L ,ina situation (w, t) to a value into the interval [0,1] such that for each truth values assigned for the terms of free variables ρ we have that V (R(τ , ... , τ )) = μ (ρ (τ ), ... , ρ (τ )) 1 n w 1 w n t t t w w V (¬ϕ) = N(V (ϕ)) t t w w w V (ϕ ∧ φ) = T(V (ϕ), V (φ)) t t t w w w V (ϕ ∨ φ) = S(V (ϕ), V (φ)) t t t w w w V (ϕ → φ) = J(V (ϕ), V (φ)) t t t The set of all situations of a world w is denoted by S and S = W × T is the set of all situations of the model. w p 9 w B (i) is the set of all belief-accessible world from the situation w by the agent i. The set of desire- and intention-accessible t t worlds have analogous denotation. ‘path(1)’ indicates the next adjacent time-point (from the current time-point). ‘paths(w )’ is the set of all paths of the world w from the time-point t. The path that originates the time-point t is denoted by p(t). FUZZY INFORMATION AND ENGINEERING 147 w w w V (ϕ ↔ φ) = E(V (ϕ), V (φ)) t t t w w w w V (∀x · (φ)) = inf {V (φ)|V (y) = V (y)∀y · (y = x)} t t t t w w w w V (∃x · (φ)) = sup{V (φ)|V (y) = V (y)∀y · (y = x)} t t t t w w V (♦ϕ) = sup{V (ϕ)|tRt )} w w V (ϕ) = inf {V (ϕ)|tRt )} w w V (ϕ) = inf {V (ϕ)|tRt and t = path(1)} t t w w w w w V (ϕU φ) = inf {{T(V (ϕ), V (¬φ))}∪{V (φ)}∪{V (¬ϕ)}|∀j, i · (t < j ≤ t , t ≤ i and j j t i j, t , i ∈ paths(w ))}, where t = max{j ∈ paths(w )|V (¬φ) ≥ k}+ 1 t t w w w w V (ϕWφ) = min(inf {T(V (ϕ), V (¬φ))|∀j · (t < j ≤ t and j, t ∈ paths(w ))}, V (φ)), j j t where t = max{j ∈ paths(w )|V (¬φ) ≥ k}+ 1 w w V (Bel (ϕ)) = inf {V (ϕ)|B(w , w )} ag t t t w w V (Des (ϕ)) = inf {V (ϕ)|D(w , w )} ag t t t w w V (Int (ϕ)) = inf {V (ϕ)|I(w , w )} ag t t t w w V (Inev(ϕ)) = inf {V (ϕ)|t ∈ paths(w )} w w V (Opt(ϕ)) = sup{V (ϕ)|t ∈ paths(w )} 1, if Suc (ag, t , t + 1) = e w i i V (Succeeds (e)) = ag 0, otherwise. 1, if Fal (ag, t , t + 1) = e w i i V (Fails (e)) = ag 0, otherwise. 1, if Suc (ag, t , t + 1) = e or Fal (ag, t , t + 1) = e w i i w i i V (Does (e)) = ag 0, otherwise. 1, if ∃t s.t.t ∈ p(t ) and Suc (ag, t − 1, t ) = e w i i j w i i V (Succeeded (e)) = ag p(t ) 0, otherwise. 1, if ∃t s.t.t ∈ p(t ) and Fal (ag, t − 1, t ) = e i i j w i i V (Failed (e)) = ag p(t ) 0, otherwise. ⎪ 1, if ∃t s.t.t ∈ p(t ) and (Suc (ag, t − 1, t ) = e i i j w i i or Fal (ag, t − 1, t ) = e) V (Done (e)) = w i i ag p(t ) 0, otherwise. 148 A. CRUZ ET AL. 1, if there exists t ∈ p s.t.V (Succeeds (e)) = 1 V (Agts (g, e)) = ag 0, otherwise. w w V (ϕ),if V (Succeeds (e)) = 1 t+1 p(t) V (Achvs (e, ϕ)) = ag 0, otherwise. Definition 2.7: A model of the fuzzy BDI Logic is a tuple M = T ,M , V where T is a fuzzy semantic, M is a model for LoRA and V is an evaluation function with respect to T . When T is k-crisp for some k wesayMof k-model. bdi Definition 2.8: Let V: S × L → [0, 1] be an evaluation function and k ∈ [0,1]atruth bdi bdi w constant. A formula ϕ ∈ L is k-true in a model M, denoted by M |= ϕ iff V (ϕ) ≥ k for each situation (w, t). Hence, when V (ϕ) ≥ k,(M, V) is said to be a model of ϕ. bdi Definition 2.9: Let ϕ be a formula of L then: bdi (1) ϕ is k-true in a situation w of a model M and evaluation V, denoted by M, V, w |= ϕ, t t if V (ϕ) ≥ k. bdi (2) ϕ is k-satisfiable in a model M and evaluation V, denoted by M, V |= ϕ, if there exists bdi a situation w such that M, V, w |= ϕ. t t bdi (3) ϕ is k-unsatisfiable in a world w of a model M and evaluation V, denoted by M, V |= / ϕ,if V (ϕ) < k for any w ∈ S . t w bdi (4) ϕ is k-true in M, denoted by M |= ϕ, if for all evaluation V and possible world w there is at least one situation w ∈ S such that V (ϕ) ≥ k, i.e. if ϕ is k-satisfiable in every t w t world w of M and evaluation V. (5) ϕ is k-false in M if it is k-unsatisfiable in every world w of M and evaluation V. (6) ϕ is a k-contigent formula in M if for all evaluation V there are worlds w and w in M w w such that V (ϕ) ≥ k and V (ϕ) < k. t t bdi (7) ϕ is k-universally valid, denoted by |= ϕ, if for all model M, evaluation V and situation bdi w ,M, V, w |= ϕ. t t bdi bdi Definition 2.10: Let L be the BDI language, ⊆ L a set of formulae of this language, bdi bdi and k ∈ (0, 1]. ϕ ∈ L is a k-semantic consequence of , denoted by |= ϕ, iff for all (w, bdi bdi t)and k-model M, if M, V, w |= then M, V, w |= ϕ, that is, in every situation in which t t k k is satisfiable, so is ϕ. bdi Definition 2.11: Let L be the BDI language, then the fuzzy BDI Logic is bdi bdi bdi Log = L , |= To complete the presentation of the fuzzy BDI Logic, we demonstrate now that it satisfies the Deduction Theorem. bdi Theorem 1: Let M be a k-model of the fuzzy BDI logic. Let ϕ and φ be a wff of the L .So bdi bdi ϕ |= φ iff |= ϕ → φ k k FUZZY INFORMATION AND ENGINEERING 149 bdi Proof: Let k be the truth constant and ϕ, φ ∈ L . bdi ⇒: Suppose that ϕ |= φ. So, by Definition 2.10, for every situation (w, t)ofthe w w w w w model, if V (ϕ) ≥ k, then V (φ) ≥ k. By Definition 2.6, V (→ φ) = J(V (ϕ), V (φ))and t t t t t w w w if V (ϕ) ≥ k then V (ϕ → φ) ≥ k, because V (φ) ≥ k and T is k-crisp. Therefore ϕ → φ. t t bdi ⇐: Suppose that |= ϕ → φ. So by Definition 2.9, for all model M and evalua- w w tion V and situation w we have that V (ϕ → φ) ≥ k and by Definition 2.6,V (ϕ t t w w w w → φ) = J(V (ϕ), V (φ)). So, since T is k-crisp, either V (ϕ) < k or V (φ) ≥ k.Thus t t t w w bdi V (φ) ≥ k whenever V (ϕ) ≥ k. Therefore ϕ |= φ. t t bdi Corollary 2.1: Let ϕ , ... , ϕ , ϕ be wff of the L .So 1 n bdi bdi ϕ , ... , ϕ |= ϕ iff ϕ , ... , ϕ |= ϕ → ϕ 1 n 1 n−1 n k k bdi Proof: Let k be the truth constant and ϕ , ... , ϕ , ϕ ∈ L . 1 n bdi ⇒: Suppose that ϕ , ... , ϕ |= ϕ. So, by Definition 2.10, for every situation (w, t) 1 n w w of the model, if V (ϕ ) ≥ k for each i = 1, ... , n, then V (ϕ) ≥ k. On the other hand, t i t for some situation (w, t) of a model, occurs that V (ϕ ) ≥ k for each i = 1, ... , n − t i w w w 1. Thus, case (a) V (ϕ ) ≥ k, then V (ϕ) ≥ k, by the hypothesis, and so V (ϕ → t n t n w w w w ϕ) = J(V (ϕ ), V (ϕ)) ≥ k.Case(b) V (ϕ ) < k, then, because T is k-crisp, V (ϕ → n t n n t t t w w bdi ϕ) = J(V (ϕ ), V (ϕ)) ≥ k. Hence ϕ , ... , ϕ |= ϕ → ϕ. n 1 n−1 n t t bdi ⇐: Suppose that ϕ , ... , ϕ |= ϕ → ϕ. So by Definitions 2.10 and 2.5 and the prop- 1 n−1 n w w erties showed in Definition 2.1, for every (w, t)suchthat V (ϕ , ... , ϕ ) ≥ k, V (ϕ) ≥ k 1 n−1 t w w w (for any value of V (ϕ )), or V (ϕ) < k (for any value of V (ϕ)). In both cases, for every (w, n t t t w w bdi t)suchthat V (ϕ , ... , ϕ ) ≥ k, V (ϕ) ≥ k. Hence ϕ , ... , ϕ |= ϕ. 1 n 1 n t t 3. Related Works According to Santos [34] a fuzzy approach is important to personality-based social exchanges in multiagent systems. In that paper was used the fuzzy logic to deal with the interaction processes between agents with different types of personalities, evaluating an exchange process using pertinence degrees. Interactions between agents are based on Piaget’s theory of social exchanges. Since social exchange values are a qualitative nature, so they could be modelled by fuzzy BDI logic. In order to structure the regulator agent decision process and the exchange strategy learning process of open multiagent systems, in [35] was proposed a combination of a par- tially observable Markov decision process (POMDP) and a hidden Markov model (HMM). That paper shows interactions between agents when cooperating/competing to achieve their individual, collective objectives. Can be interesting analyse the possibility of using an adaptation of fuzzy BDI logic for interaction process. Casali, Godo and Sierra in [36,37] propose the g-BDI (graded BDI) architecture to repre- sent and reason through gradual notions of desires and intentions, including a complete logical formalisation. The works show a framework for studying and developing this type of agents. The graded BDI considers the following characteristics: (i) beliefs degrees; (ii) degrees of positive or negative desires; (iii) intention degrees. An agent with different types of behaviour can be modelled with g-BDI, based on the representation and interaction of 150 A. CRUZ ET AL. these characteristics. Moreover, the approach modal fuzzy is used to represent and reason about different degrees of mental attitudes and a multi-context system (MCS) was con- sidered to integrate processes between g-BDI agents defining mental contexts, functional contexts and a set of bridge rules. A MCS for a g-BDI agent is defined as a tuple with (i) the mental contexts represent: beliefs context (BC), desires context (DC) and intentions context (IC); (ii) two functional contexts are used for planning and communication; (iii) a suitable set of rules encode to a particular pattern of interaction between beliefs, desires and intentions. Soundness and completeness was proved for desires context, the axiomatization is correct with respect to the defined semantics and it is complete as well for finite theories of modal formulae. In [37] was developed a graded BDI agent framework and a case of study was devel- oped using this framework to a recommendation system applied to tourism, showing the flexibility and performance of a g-BDI model. A BDI software applications in the simulation area of human behaviour is explored in [38]. This work develops a study, exploring the differences in an approach based on classical rules and fuzzy rules. A fuzzy approach is made using BDI agents. It developed a game that showing the efficiency and realistic approach using BDI fuzzy systems, most adapting to human behaviour. The work does not explore mathematical concepts and an appropriate formalisation. In [39], the authors strengthen the use of a fuzzy BDI semantic. They state that intelligent agents’ models which do not admit degrees of mental attitudes results systems incapable to take account of much of the useful information which helps to guide the human reason- ing about the world. Moreover, rational agents (especially human being) believe or desire some states more than others, similarly, to intend something (regarding the common sense of the intention notion). In the real world we often must deal with different levels of confi- dence in our beliefs, desires, and intentions. For example, it is natural for a human to believe that he is 30 and hungry, at the same time, consequently he will desire to drink and eat something with different degrees of will. These degrees of will are determined considering what he believes to be his greater necessity at the moment and he will commit with one of the mental states: either no more 30 or no more hungry. We often lead with this type of decision-making and the fuzzy BDI semantics, defined in this paper, can perfectly model it. Thus, the idea of extending the BDI model to a fuzzy BDI model or at least to admit a degree to reason about rational agency, is not new. Some works are related to these pur- poses – see [39–44] as examples. Although relevant works consider degrees in multiagent systems and they solve specific problems. 4. Final Remarks In the initial of 1990s, Rao and Georgeff, in [6], claim that their BDI Logic was incomplete with respect to deliberation process and reconsideration and override of intention. The authors also affirm that such problems could be solved adding to the BDI logic, a decision-theoretic technique. Such decision technique could be to map a utility for each course of action, or to add a fuzzy degree of truth for each sentence in the system, or even to employ Baysean methods. To Add a fuzzy degree in the semantics of a BDI logic is an interesting solution once that we can solve the cited limitations in the same level in which they appear. FUZZY INFORMATION AND ENGINEERING 151 With a fuzzy BDI logic, it is possible to make the revision of beliefs, desires and intentions by discarding the mental attitudes whose truth degree are less than a pre-defined α number (α-cut concept). The deliberation process, the intention reconsideration and the override of intention could be easily implemented by searching for the greatest agent’s desire to become the new intention. Moreover, all those decision process could be improved by a fuzzy Inference System. This paper tries to establish the concepts related to BDI Syntax where a language about an alphabet and a set of grammatical rules was defined. As far as Fuzzy BDI Semantics is concerned a fuzzy semantic for a propositional language, an evaluation function V,andaM of fuzzy BDI Logic model are described. This paper does not address the proofs of soundness and completeness. In the future we intend to expand this study by addressing some formal theories for BDI syntax. It is necessary to show some results of soundness and completeness for some fuzzy semantics, tried to characterise these results according to the fuzzy semantics of this paper. In addition, it also must extend the fuzzy BDI logic for a lattice-valued (fuzzy) BDI logic, i.e. a BDI logic where the truth degree took value in an arbitrary lattice. Beyond of the contribution to the computational logic area – we propose a new fuzzy modal logic, and we define a new BDI logic with the limits between syntax and seman- tics clear and formally defined –, the fuzzy BDI semantics, defined in this paper, can be employed to solve a wide range of AI representation problems to model, through a logi- cal apparatus: the deliberation process, the belief and desire revision, the reconsideration and override of intention. To make the BDI model more faithful to a representation of the human being reasoning was employed the approximate reasoning in the BDI model. Disclosure statement No potential conflict of interest was reported by the author(s). Funding This work was supported by the National Council for Scientific and Technological Development (CNPq) [grant number 307781/2016-0 and 312053/2018-5]. Notes on Contributors Anderson Cruz received his MSc and PhD degrees in Computer Science from the Federal University of Rio Grande do Norte (UFRN), Natal, Brazil, in 2008 and 2012. Currently, he is an Assistant Professor at UFRN. In recent years, he took on the positions of Manager of a business incubator, Director of the Metrópole Digital Technology Park, and President of the Potiguar Network of Incubators and Tech- nology Parks. His research interests include fuzzy mathematics, non-classical logics, and policies and innovation management. André V. dos Santos received the MSc degree in Computer Science from Catholic University of Pelotas, Brazil, in 2008 and is currently a PhD Student at the Federal University of Rio Grande (FURG). His research interests include fuzzy sets theory, artificial intelligence, aggregation and preaggregation functions, clustering, social choice and multiagent systems. Regivan H. N. Santiago received his MSc and PhD degrees in Computer Science from the Federal University of Pernambuco (UFPE), Recife, Brazil, in 1995 and 1999, respectively. He is currently full 152 A. CRUZ ET AL. professor at Federal University of Rio Grande do Norte UFRN. His interests include fuzzy sets and fuzzy logics, interval mathematics, logics, domain theory, topology, theory of computation and semantics. Benjamin Bedregal received his MSc and PhD degrees in computer sciences from the Federal Univer- sity of Pernambuco, Recife, Brazil, in 1987 and 1996, respectively. In 1996, he became an Assistant Professor with the Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, Brazil, where he is currently a Full Professor. Associate Editor of IEEE Trans. on Fuzzy Systems, Journal of Fuzzy Extension and Applications and TEMA – Trends in Applied and Com- putational Mathematics. His research interests include non-standard fuzzy sets theory, aggregation and pre-aggregation functions, clustering, fuzzy mathematics, and fuzzy automata. References [1] Bratman ME. Intentions, plans and practical reason. Cambridge (MA): Harvard University Press; [2] Bratman ME, Israel D, Pollack ME. Plans and resource-bounded practical reasoning. Comput Intell. 1988;4:349–355. [3] Hoek W, Wooldridge M. Towards a logic of rational agency. Log J IGPL. 2003;11:135–159. [4] Cohen PR, Levesque HJ. Intention is choice with commitment. Artif Intell. 1990;42:213–261. [5] Rao AS, Georgeff MP. Modelling rational agents within a BDI architecture. Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning; 1991. p. 473–484. [6] Rao AS, Georgeff MP. Intentions and rational commitment. Proceedings of the First Pacific Rim International Conference on Artificial Intelligence; Nagoya, Japan; 1993. [7] Wooldridge M. Reasoning about rational agents. Cambridge (MA): MIT Press; 2000. [8] Searle JR. Intentionality. An essay in the philosophy of mind. New York: Cambridge University Press; 1983. [9] Bordini RH, Hubner JF, Wooldridge M. Programming multi-agent systems in AgentSpeak using Jason. Chichester: John Wiley & Sons; 2007. [10] Busetta P, Ronnquist R, Hodgson A, et al. JACK intelligent agents – components for intelligent agents in Java. Technical report. Melbourne: Agent Oriented Software; 1998. [11] d’Inverno M, Kinny D, Luck M, et al. A formal specification of dMARS. Proceedings of the 4th International Workshop on Intelligent Agents IV, Agent Theories, Architectures, and Languages; 1998. p. 155–176. [12] d’Inverno M, Luck M. Engineering AgentSpeak(L): a formal computational model. J Logic Com- put. 1998;8(3):233–260. [13] Padgham L, Winikoff M. The prometheus methodology. In: Multiagent systems, artificial soci- eties, and simulated organizations. Vol. 11. 2004. p. 217–234. [14] Morgan CG. Two values, three values, many values, no values. In: Fitting M, Orłowska E, editors. Beyond two: theory and applications of multiple-valued logic. Berlin: Springer; 2003. p. 349–374. [15] Bergmann M. An Introduction to many-valued and fuzzy logic: semantics, algebras and deriva- tion systems. Cambridge: Cambridge University Press; 2008. [16] Caleiro C, Marcos J, Volpe M. Bivalent semantics, generalized compositionality and analytic classic-like tableaux for finite-valued logics. Theor Comput Sci. 2015;603:84–110. [17] Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–353. [18] Baczyński M, Jayaram B. Fuzzy implications. Vol. 231. Springer; 2008. ISBN:978-3-540-69080-1. [19] Chellas B. Modal logic: an introduction. Cambridge: Cambridge University Press; 1980. [20] Bedregal BC, Cruz AP. A characterization of classic-like fuzzy semantics logical as a propositional fuzzy logic. Log J IGPL. 2008;16(4):357–370. [21] Fitting M. Many-valued modal logics. Fundam Inform. 1991;15:235–254. [22] Santiago RHN, Bedregal BC, Madeira A. On interval dynamic logic: introducing quasi-action lattices. Sci Comput Program 2019;175:1–16. [23] Dodo A, Marcos J, Bergamaschi FB. On classic-like fuzzy modal logics. Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS); 2013. p. 1256–1261. FUZZY INFORMATION AND ENGINEERING 153 [24] Hájek P, Harmancová D. A many-valued modal logics. Proceedings of International Confer- ence on Information Processing and Management of Uncertain in Knowledge-Based Systems. p. 1021–1024. [25] Hájek P. Metamathematics of fuzzy logic. Series: trends in logic. Vol. 4. Dordrecht: Kluwer; 1998. [26] Zhang Z, Sui Y, Cao C. Fuzzy reasoning based on propositional modal logic. Proceedings of the Fourth Internat. Conf. on Rough Sets and Current Trends in Computing. Vol. 3066; 2004. p. 109–115. [27] Zhang Z, Sui Y, Cao C, et al. A formal fuzzy reasoning system and reasoning mechanism based on propositional modal logic. Theor Comput Sci. 2006;368:149–160. [28] Bedregal BC, Santiago RN, Benevides MF, et al. K, T and D-like fuzzy Kripke models. 30th North American Fuzzy Information Processing Society Annual Conference, NAFIPS; 2011.p.1–5. [29] Bedregal BC, Cruz AP. Propositional logic as a propositional fuzzy logic. Electron Notes Theor Comput Sci. 2006;143:5–12. [30] Caicedo X, Rodríguez RO. Bi-modal Gödel logic over [0; 1]-valued Kripke frames. J Logic Comput. 2015;25(1):37–55. [31] Callejas C, Marcos J, Bedregal BC. On some subclasses of the Fodor-Roubens fuzzy bi-implication. Lect Notes Comput Sci. 2012;7456:206–215. [32] Cruz AP, Bedregal BC, Santiago RN. On the Boolean-like Law I(x, I(y, x)) = 1. Int J Uncertain Fuzziness Knowl-Based Syst. 2014;22(2):205–215. [33] Cruz AP, Bedregal BC, Santiago RN. On the characterizations of fuzzy implications satisfying I(x, I(y, z)) = I(I(x, y), I(x, z)). Approx Reason. 2018;93(1):261–276. [34] Santos AV, Dimuro GP, Bedregal BC, et al. Fuzzy evaluation of social exchanges between personality-based agents. 14th Portuguese Conference on Artificial Intelligence – EPIA ‘2009/Social Simulation and Modelling – SSM. New Trends in Artificial Intelligence; 2009. p. 451–462. [35] Dimuro GP, Costa ACR. Regulating social exchanges in open MAS: the problem of reciprocal conversions between POMDPs and HMMs. Inf Sci (Ny). 2015;323:16–33. [36] Casali A, Godo L, Sierra C. g-BDI: a graded intensional agent model for practical reasoning. Model Decis Artif Intell. 2009;5861:5–10. [37] Casali A, Godo L, Sierra C. A graded BDI agent model to represent and reason about preferences. Artif Intell. 2011;175:1468–1478. [38] Vu TM, Siebers P-O, Wagner C. Comparison of crisp systems and fuzzy systems in agent-based simulation: a case study of soccer penalties. 13th UK Workshop on Computational Intelligence (UKCI); 2013. p. 54–61. [39] Parsons S, Giorgini P. An approach to using degrees of belief in BDI agents. In: Information, uncertainty and fusion. The Springer International Series in Engineering and Computer Science. Vol. 516. 2000. p. 81–92. [40] Blee J, Billington D, Governatori G, et al. Levels of modalities for BDI logic. IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology. Vol. 3; 2008. p. 647–650. [41] Carbo J, Molina JM, Davila J. A BDI agent architecture for reasoning about reputation. IEEE International Conference on Systems, Man, and Cybernetics. Vol. 2; 2001. p. 817–822. [42] Dragoni AF, Giorgini P. Belief revision through the belief function formalism in a multiagent environment. Intelligent Agents III. LNCS. Vol. 1193; 1997. [43] Parsons S, Pettersson O, Saffiotti A, et al. Intention reconsideration in theory and practice. Proceedings of Fourteenth European Conference on Artificial Intelligence. IOS Press; 2000. p. 378–382. [44] Shen S, O’Hare GMP, Collier R. Decision-making of BDI agents, a fuzzy approach. Proceed- ings of the 4th International Conference on Computer and Information Technology; 2004. p. 1022–1027. [45] Dimuro GP, Farias GP, Peter GD, et al. A BDI-fuzzy agent model for exchanges of non-economic services based on the social exchange theory. Brazilian Conference on Intelligent Systems (BRACIS); 2013. p. 26–32.
Fuzzy Information and Engineering – Taylor & Francis
Published: Apr 3, 2021
Keywords: Agents; fuzzy logic; BDI logic; LoRA
You can share this free article with as many people as you like with the url below! We hope you enjoy this feature!
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.