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A Reconstruction of Default Conditionals within Epistemic Logic

Koutras Costas D., Moyzes Christos, Rantsoudis Christos

Fundamenta Informaticae

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2019

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Vol. 166, nr 2

167--197

EN

Default conditionals are statements that express a condition of normality, in the form ‘if φ then normally ψ’ and are of primary importance in Knowledge Representation. There exist modal approaches to the construction of conditional logics of normality. Most of them are built on notions of preference among possible worlds, corresponding to the semantic intuition that φ ⇒ ψ is true in a situation if in the most preferred (most ‘normal’) situations in which φ is true, ψ is also true. It has been noticed that there exist natural epistemic readings of a default conditional, but this direction has not been thoroughly explored. A statement of the form ‘something known to be a bird, that can be consistently believed to fly, does fly’ involves well-known epistemic attitudes and allows the possibility of defining defaults within the rich framework of Epistemic Logic. We pursue this direction here and proceed to define conditionals within KBE, a recently introduced S4.2-based modal logic of knowledge, belief and estimation. In this logic, knowledge is a normal S4 operator, belief is a normal KD45 operator and estimation is a non-normal operator interpreted as a ‘majority’ quantifier over the set of epistemically alternative situations. We define and explore various conditionals using the epistemic operators of KBE, capturing φ ⇒ ψ in various ways, including ‘according to the agent’s knowledge, an estimation that φ is true implies the estimation that (φ∧ψ) is true’ or ‘if φ is known and there is no reason to believe ¬ψ then ψ can be plausibly inferred’. Overall, we define here three nonmonotonic default conditionals, one conditional satisfying monotonicity (strengthening the antecedent) and two nonmonotonic conditionals that do not satisfy the ubiquitous axiom ID (reflexivity). Our project provides concrete evidence that the machinery of epistemic logic can be exploited for the study of default conditionals.

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A Tractable Rule Language in the Modal and Description Logic that Combines CPDL with Regular Grammar Logic

Nguyen L. A.

Fundamenta Informaticae

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2016

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Vol. 143, nr 1/2

113--139

EN

Combining CPDL (Propositional Dynamic Logic with Converse) and regular grammar logic results in an expressive modal logic denoted by CPDLreg. This logic covers TEAMLOG, a logical formalism used to express properties of agents’ cooperation in terms of beliefs, goals and intentions. It can also be used as a description logic for expressing terminological knowledge, in which both regular role inclusion axioms and CPDL-like role constructors are allowed. In this paper, we develop an expressive and tractable rule language called Horn-CPDLreg. As a special property, this rule language allows the concept constructor “universal restriction” to appear on the left hand side of general concept inclusion axioms. We use a special semantics for Horn-CPDLreg that is based on pseudo-interpretations. It is called the constructive semantics and coincides with the traditional semantics when the concept constructor “universal restriction” is disallowed on the left hand side of concept inclusion axioms or when the language is used as an epistemic formalism and the accessibility relations are serial. We provide an algorithm with PTIME data complexity for checking whether a knowledge base in Horn-CPDLreg has a pseudo-model. This shows that the instance checking problem in Horn-CPDLreg with respect to the constructive semantics has PTIME data complexity.

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Consistency-based Revision of Structured Belief Bases

Korpusik M., Łukaszewicz W., Madalińska-Bugaj E.

Fundamenta Informaticae

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2015

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Vol. 136, nr 4

381--404

EN

In this paper we extend a consistency-based approach (originally introduced by Delgrande and Schaub) to belief revision for structured belief bases. We explicitly distinguish between observations, i.e., facts that an epistemic agent observes or is being told, and rules representing general knowledge about the considered world. When new information becomes available respective sets are being altered in a different way to preserve parts of knowledge during the revision process. Such an approach allows us to deal with difficult and complex scenarios, involving defeasible information and derivation filtering, with common-sense results.