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Igor Sedlár

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7 papers

2 author rows

FLAP Journal 2025 Journal Article

Algebras for Relevant Reasoners

Igor Sedlár

The informational interpretations of relevant logic suggest that it provides a natural framework for the development of epistemic logic. This paper proposes a simple extension of relevant modal logic to formalise reasoning about relevant reasoners situated in classical worlds. This approach avoids many of the tech- nical challenges of previous proposals and allows for straightforward algebraic generalisation. The main technical result is a representation theorem for a class of relevant algebras, which provides a solid foundation for further exploration of relevant epistemic logic. 2020 Mathematics Subject Classification. Primary: 03B47, Secondary: 03B42, 03B45.

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TARK Conference 2025 Conference Paper

Complexity of Łukasiewicz Modal Probabilistic Logics

Daniil Kozhemiachenko
Igor Sedlár

Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the modal {\L}ukasiewicz many-valued logic. These logics are shown to be capable of expressing nuanced probabilistic concepts, including upper and lower probabilities. Our main contribution is a PSPACE-completeness result for two variants of the local consequence problem, providing a precise computational characterisation.

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TARK Conference 2023 Conference Paper

Epistemic Logics of Structured Intensional Groups

Marta Bílková
Igor Sedlár

Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change its extension from world to world. Several authors have considered versions of the intensional group framework where group-specifying properties are articulated using structured terms of a language, such as the language of Boolean algebras or of description logic. In this paper we formulate a general semantic framework for epistemic logics of structured intensional groups, develop the basic theory leading to completeness-via-canonicity results, and show that several frameworks presented in the literature correspond to special cases of the general framework.

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KR Conference 2021 Conference Paper

Decidability and Complexity of Some Finitely-valued Dynamic Logics

Igor Sedlár

Propositional Dynamic Logic, PDL, is a well known modal logic formalizing reasoning about complex actions. We study many-valued generalizations of PDL based on relational models where satisfaction of formulas in states and accessibility between states via action execution are both seen as graded notions, evaluated in a finite Łukasiewicz chain. For each n>1, the logic PDŁn is obtained using the n-element Łukasiewicz chain, PDL being equivalent to PDŁ2. These finitely-valued dynamic logics can be applied in formalizing reasoning about actions specified by graded predicates, reasoning about costs of actions, and as a framework for certain graded description logics with transitive closure of roles. Generalizing techniques used in the case of PDL we obtain completeness and decidability results for all PDŁn. A generalization of Pratt's exponential-time algorithm for checking validity of formulas is given and EXPTIME-hardness of each PDŁn validity problem is established by embedding PDL into PDŁn.

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LORI Conference 2021 Conference Paper

Situated Epistemic Updates

Igor Sedlár
Andrew Tedder

Abstract One way to model epistemic states of agents more realistically is to represent these states by sets of situations rather than possible worlds. In this paper we discuss representations of epistemic update in terms of situations. After linking epistemic update based on deleting epistemic accessibility arrows with update of situations, we discuss two specific kinds of public epistemic update; monotonic update in intuitionistic dynamic epistemic logic, and non-monotonic update in substructural dynamic epistemic logic. Our investigation is mainly conceptual, but leads to completeness results using reduction axioms, and lays the groundwork for future investigation into the concept of situated epistemic update.

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LORI Conference 2019 Conference Paper

First Degree Entailment with Group Attitudes and Information Updates

Igor Sedlár
Vít Puncochár
Andrew Tedder

Abstract We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif. Intell. 79, 203–240, 1995) by adding operators for universal and common knowledge in a group of agents, and with a formalization of information update using a generalized version of the left division connective of the non-associative Lambek calculus. We provide sound and complete axiomatizations of the basic logic with the group operators and the basic logic with group operators and updates. Both logics are shown to be decidable.

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LORI Conference 2017 Conference Paper

Substructural Logics for Pooling Information

Vít Puncochár
Igor Sedlár

Abstract This paper puts forward a generalization of the account of pooling information – offered by standard epistemic logic – based on intersection of sets of possible worlds. Our account is based on information models for substructural logics and pooling is represented by fusion of information states. This approach yields a representation of pooling related to structured communication within groups of agents. It is shown that the generalized account avoids some problematic features of the intersection-based approach. Our main technical result is a sound and complete axiomatization of a substructural epistemic logic with an operator expressing pooling.

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