Author name cluster

Marta Bílková

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

5 papers

2 author rows

TARK Conference 2025 Conference Paper

Modal Logic for Reasoning About Uncertainty and Confusion

Marta Bílková
Thomas M. Ferguson
Daniil Kozhemiachenko

We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we expand G\"odel modal logic KG with the involutive negation ~ defined as v(~A, w)=1-v(A, w). We provide semantics with the finite model property for our new logic that we call KG_inv and show its equivalence to the standard semantics over [0, 1]-valued Kripke models. Namely, we show that a formula is valid in the standard semantics of KG_inv iff it is valid in the new semantics. Using this new semantics, we construct a constraint tableaux calculus for KG_inv that allows for an explicit extraction of countermodels from complete open branches and then employ the tableaux calculus to obtain the PSPACE-completeness of the validity in KG_inv.

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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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JELIA Conference 2023 Conference Paper

Non-standard Modalities in Paraconsistent Gödel Logic

Marta Bílková
Sabine Frittella
Daniil Kozhemiachenko

Abstract We introduce a paraconsistent expansion of the Gödel logic with a De Morgan negation \(\lnot \) and modalities \(\blacksquare \) and \(\blacklozenge \). We dub the logic \(\textsf{G}^{2\pm }_{\blacksquare, \blacklozenge }\) and equip it with Kripke semantics on frames with two (possibly fuzzy) relations: \(R^+\) and \(R^-\) (interpreted as the degree of trust in affirmations and denials by a given source) and valuations \(v_1\) and \(v_2\) (positive and negative support) ranging over [0, 1] and connected via \(\lnot \). We motivate the semantics of \(\blacksquare \phi \) (resp. , \(\blacklozenge \phi \) ) as infima (suprema) of both positive and negative supports of \(\phi \) in \(R^+\) - and \(R^-\) -accessible states, respectively. We then prove several instructive semantical properties of \(\textsf{G}^{2\pm }_{\blacksquare, \blacklozenge }\). Finally, we devise a tableaux system for \(\textsf{G}^{2\pm }_{\blacksquare, \blacklozenge }\) over finitely branching frames and establish the complexity of satisfiability and validity.

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TARK Conference 2021 Conference Paper

Revisiting Epistemic Logic with Names

Marta Bílková
Zoé Christoff
Olivier Roy

This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional "names". We make three contributions. First, we study its model theory, providing adequate notions of bisimulation and frame morphisms, and use them to study the logic's expressive power and definability. Second, we show that the logic has a natural neighborhood semantics, which in turn allows to show that the axiomatization in [10] does not rely on possibly controversial introspective properties of knowledge. Finally, we extend the logic with common and distributed knowledge operators, and provide a sound and complete axiomatization for each of these extensions. These results together put the original epistemic logic with names in a more modern context and opens the door for a logical analysis of epistemic phenomena where group membership is uncertain or variable.

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TCS Journal 2014 Journal Article

Proof systems for Moss' coalgebraic logic

Marta Bílková
Alessandra Palmigiano
Yde Venema

We study Gentzen-style proof theory of the finitary version of the coalgebraic logic introduced by L. Moss. The logic captures the behaviour of coalgebras for a large class of set functors. The syntax of the logic, defined uniformly with respect to a finitary coalgebraic type functor T, uses a single modal operator ∇ T of arity given by the functor T itself, and its semantics is defined in terms of a relation lifting functor T ¯. An axiomatization of the logic, consisting of modal distributive laws, has been given together with an algebraic completeness proof in work of C. Kupke, A. Kurz and Y. Venema. In this paper, following our previous work on structural proof theory of the logic in the special case of the finitary powerset functor, we present cut-free, one- and two-sided sequent calculi for the finitary version of Moss' coalgebraic logic for a general finitary functor T in a uniform way. For the two-sided calculi to be cut-free we use a language extended with the boolean dual of the nabla modality.

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