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The Epistemic Logic Behind the Game Description Language

AAAI Conferences

A general game player automatically learns to play arbitrary new games solely by being told their rules. For this purpose games are specified in the game description language GDL, a variant of Datalog with function symbols and a few known keywords. In its latest version GDL allows to describe nondeterministic games with any number of players who may have imperfect, asymmetric information. We analyse the epistemic structure and expressiveness of this language in terms of epistemic modal logic and present two main results: The operational semantics of GDL entails that the situation at any stage of a game can be characterised by a multi-agent epistemic (i.e., S5-) model; (2) GDL is sufficiently expressive to model any situation that can be described by a (finite) multi-agent epistemic model.


Revisiting Semantics for Epistemic Extensions of Description Logics

AAAI Conferences

Epistemic extensions of description logics (DLs) have been introduced several years ago in order to enhance expressivity and querying capabilities of these logics by knowledge base introspection. We argue that unintended effects occur when imposing the traditionally employed semantics on the very expressive DLs that underly the OWL 1 and OWL 2 standards. Consequently, we suggest a revised semantics that behaves more intuitively in these cases and coincides with the traditional semantics of less expressive DLs. Moreover, we introduce a way of answering epistemic queries to OWL knowledge bases by a reduction to standard OWL reasoning. We provide an implementation of our approach and present first evaluation results.


An Epistemic Halpern-Shoham Logic

AAAI Conferences

We define a family of epistemic extensions of Halpern-Shoham logic for reasoning about temporal-epistemic properties of multi-agent systems. We exemplify their use and study the complexity of their model checking problem. We show a range of results ranging from PTIME to PSPACE-hard depending on the logic considered.


Founded (Auto)Epistemic Equilibrium Logic Satisfies Epistemic Splitting

arXiv.org Artificial Intelligence

In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.


PDT Logic: A Probabilistic Doxastic Temporal Logic for Reasoning about Beliefs in Multi-agent Systems

Journal of Artificial Intelligence Research

We present Probabilistic Doxastic Temporal (PDT) Logic, a formalism to represent and reason about probabilistic beliefs and their temporal evolution in multi-agent systems. This formalism enables the quantification of agents beliefs through probability intervals and incorporates an explicit notion of time. We discuss how over time agents dynamically change their beliefs in facts, temporal rules, and other agents beliefs with respect to any new information they receive. We introduce an appropriate formal semantics for PDT Logic and show that it is decidable. Alternative options of specifying problems in PDT Logic are possible. For these problem specifications, we develop different satisfiability checking algorithms and provide complexity results for the respective decision problems. The use of probability intervals enables a formal representation of probabilistic knowledge without enforcing (possibly incorrect) exact probability values. By incorporating an explicit notion of time, PDT Logic provides enriched possibilities to represent and reason about temporal relations.