Logics of Temporal-Epistemic Actions

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in Dynamic Epistemic Logic

Representing and Reasoning about Dynamic Multi-Agent Domains: An Action Language Approach

abstract: Reasoning about actions forms the basis of many tasks such as prediction, planning, and diagnosis in a dynamic domain. Within the reasoning about actions community, a broad class of languages, called action languages, has been developed together with a methodology for their use in representing and reasoning about dynamic domains. With a few notable exceptions, the focus of these efforts has largely centered around single-agent systems. Agents rarely operate in a vacuum however, and almost in parallel, substantial work has been done within the dynamic epistemic logic community towards understanding how the actions of an agent may effect not just his own knowledge and/or beliefs, but those of his fellow agents as well. What is less understood by both communities is how to represent and reason about both the direct and indirect effects of both ontic and epistemic actions within a multi-agent setting. This dissertation presents ongoing research towards a framework for representing and reasoning about dynamic multi-agent domains involving both classes of actions. The contributions of this work are as follows: the formulation of a precise mathematical model of a dynamic multi-agent domain based on the notion of a transition diagram; the development of the multi-agent action languages mA+ and mAL based upon this model, as well as preliminary investigations of their properties and implementations via logic programming under the answer set semantics; precise formulations of the temporal projection, and planning problems within a multi-agent context; and an investigation of the application of the proposed approach to the representation of, and reasoning about, scenarios involving the modalities of knowledge and belief.Dissertation/ThesisDoctoral Dissertation Computer Science 201

A family of graded epistemic logics

Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Martí-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceió, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).publishe

Using fuzzy logic to integrate neural networks and knowledge-based systems

Outlined here is a novel hybrid architecture that uses fuzzy logic to integrate neural networks and knowledge-based systems. The author's approach offers important synergistic benefits to neural nets, approximate reasoning, and symbolic processing. Fuzzy inference rules extend symbolic systems with approximate reasoning capabilities, which are used for integrating and interpreting the outputs of neural networks. The symbolic system captures meta-level information about neural networks and defines its interaction with neural networks through a set of control tasks. Fuzzy action rules provide a robust mechanism for recognizing the situations in which neural networks require certain control actions. The neural nets, on the other hand, offer flexible classification and adaptive learning capabilities, which are crucial for dynamic and noisy environments. By combining neural nets and symbolic systems at their system levels through the use of fuzzy logic, the author's approach alleviates current difficulties in reconciling differences between low-level data processing mechanisms of neural nets and artificial intelligence systems

Reasoning about Actions with Temporal Answer Sets

In this paper we combine Answer Set Programming (ASP) with Dynamic Linear Time Temporal Logic (DLTL) to define a temporal logic programming language for reasoning about complex actions and infinite computations. DLTL extends propositional temporal logic of linear time with regular programs of propositional dynamic logic, which are used for indexing temporal modalities. The action language allows general DLTL formulas to be included in domain descriptions to constrain the space of possible extensions. We introduce a notion of Temporal Answer Set for domain descriptions, based on the usual notion of Answer Set. Also, we provide a translation of domain descriptions into standard ASP and we use Bounded Model Checking techniques for the verification of DLTL constraints.Comment: To appear in Theory and Practice of Logic Programmin

A Path in the Jungle of Logics for Multi-Agent Systems: on the Relation between General Game-Playing Logics and Seeing-To-It-That Logics

In the recent years, several concurrent logical systems for reasoning about agency and social interaction and for representing game properties have been proposed. The aim of the present paper is to put some order in this 'jungle' of logics by studying the relationship between the dynamic logic of agency DLA and the game description language GDL. The former has been proposed as a variant of the logic of agency STIT by Belnap et al. in which agents' action are named, while the latter has been introduced in AI as a formal language for reasoning about general game-playing. The paper provides complexity results for the satisfiability problems of both DLALogic and GDL as well as a polynomial embedding of GDL into DLA

Reasoning about obligations in Obligationes : a formal approach.

Despite the appearance of `obligation' in their name, medieval obligational dispu- tations between an Opponent and a Respondent seem to many to be unrelated to deontic logic. However, given that some of the example disputations found in me- dieval texts involve Respondent reasoning about his obligations within the context of the disputation, it is clear that some sort of deontic reasoning is involved. In this paper, we explain how the reasoning diers from that in ordinary basic deontic logic, and dene dynamic epistemic semantics within which the medieval obligations can be expressed and the examples evaluated. Obligations in this framework are history- based and closely connected to action, thus allowing for comparisons with, e.g., the knowledge-based obligations of Pacuit, Parikh, and Cogan, and stit-theory. The con- tributions of this paper are twofold: The introduction of a new type of obligation into the deontic logic family, and an explanation of the precise deontic concepts involved in obligationes

Reasoning about Obligations in Obligationes: A Formal Approach

Despite the appearance of `obligation' in their name, medieval obligational dispu- tations between an Opponent and a Respondent seem to many to be unrelated to deontic logic. However, given that some of the example disputations found in me- dieval texts involve Respondent reasoning about his obligations within the context of the disputation, it is clear that some sort of deontic reasoning is involved. In this paper, we explain how the reasoning diers from that in ordinary basic deontic logic, and dene dynamic epistemic semantics within which the medieval obligations can be expressed and the examples evaluated. Obligations in this framework are history- based and closely connected to action, thus allowing for comparisons with, e.g., the knowledge-based obligations of Pacuit, Parikh, and Cogan, and stit-theory. The con- tributions of this paper are twofold: The introduction of a new type of obligation into the deontic logic family, and an explanation of the precise deontic concepts involved in obligationes