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Michał Zawidzki

Publications and source records attributed to Michał Zawidzki.

7 recordsLinked to original sources
arXiv2025

Description Logics with Two Types of Definite Descriptions: Complexity, Expressiveness, and Automated Deduction

Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an alternative to proper names (IDs), which lack semantic content and serve merely as placeholders. In this paper, we introduce two extensions of the well-known description logic $\mathcal{ALC}$ with local and global definite descriptions, denoted $\mathcal{ALC}ι_L$ and $\mathcal{ALC}ι_G$, respectively. We define appropriate bisimulation notions for these logics, enabling an analysis of their expressiveness. We show that although both logics share the same tight ExpTime complexity bounds for concept and ontology satisfiability, $\mathcal{ALC}ι_G$ is strictly more expressive than $\mathcal{ALC}ι_L$. Moreover, we present tableau-based decision procedures for satisfiability in both logics, provide their implementation, and report on a series of experiments. The empirical results demonstrate the practical utility of the implementation and reveal interesting correlations between performance and structural properties of the input formulas.

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arXiv2024

Definite Descriptions and Hybrid Tense Logic

We provide a version of first-order hybrid tense logic with predicate abstracts and definite descriptions as the only non-rigid terms. It is formalised by means of a tableau calculus working on sat-formulas. A particular theory of DD exploited here is essentially based on the approach of Russell, but with descriptions treated as genuine terms. However, the reductionist aspect of the Russellian approach is retained in several ways. Moreover, a special form of tense definite descriptions is formally developed. A constructive proof of the interpolation theorem for this calculus is given, which is an extension of the result provided by Blackburn and Marx.

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arXiv2024

Hybrid Modal Operators for Definite Descriptions

In this paper, we study computational complexity and expressive power of modal operators for definite descriptions, which correspond to statements `the modal world which satisfies formula \(varphi\)'. We show that adding such operators to the basic (propositional) modal language has a price of increasing complexity of the satisfiability problem from PSpace to ExpTime. However, if formulas corresponding to descriptions are Boolean only, there is no increase of complexity. Furthermore, we compare definite descriptions with the related operators from hybrid and counting logics. We prove that the operators for definite descriptions are strictly more expressive than hybrid operators, but strictly less expressive than counting operators. We show that over linear structures the same expressive power results hold as in the general case; in contrast, if the linear structures are isomorphic to integers, definite descriptions become as expressive as counting operators.

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arXiv2022

Proceedings of the 10th International Conference on Non-Classical Logics. Theory and Applications

Non-Classical Logics. Theory and Applications (NCL) is an international conference aimed at presenting novel results and survey works in widely understood non-classical logics and their applications. This year's edition was also an opportunity to celebrate the 50th anniversary of the logic journal Bulletin of the Section of Logic (BSL), established in 1971 and since then published by the University of Lodz. On this occassion a number of renowned researchers having bonds with BSL were asked to deliver invited talks. Additionally, during the conference a special session was held commemorating J. Michael Dunn, outstanding logician and collecting editor of BSL, who passed away in 2021. Finally, collocated with the conference were three workshops devoted to, subsequently, non-Fregean logics, relating logics, and formal ontology, as well as a tutorial on graded logic.

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arXiv2021

Tableaux for Free Logics with Descriptions

The paper provides a tableau approach to definite descriptions. We focus on several formalizations of the so-called minimal free description theory (MFD) usually formulated axiomatically in the setting of free logic. We consider five analytic tableau systems corresponding to different kinds of free logic, including the logic of definedness applied in computer science and constructive mathematics for dealing with partial functions (here called negative quasi-free logic). The tableau systems formalise MFD based on PFL (positive free logic), NFL (negative free logic), PQFL and NQFL (the quasi-free counterparts of the former ones). Also the logic NQFLm is taken into account, which is equivalent to NQFL, but whose language does not comprise the existence predicate. It is shown that all tableaux are sound and complete with respect to the semantics of these logics.

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arXiv2021

Tableau-based decision procedure for non-Fregean logic of sentential identity

Sentential Calculus with Identity (SCI) is an extension of classical propositional logic, featuring a new connective of identity between formulas. In SCI two formulas are said to be identical if they share the same denotation. In the semantics of the logic, truth values are distinguished from denotations, hence the identity connective is strictly stronger than classical equivalence. In this paper we present a sound, complete, and terminating algorithm deciding the satisfiability of SCI-formulas, based on labelled tableaux. To the best of our knowledge, it is the first implemented decision procedure for SCI which runs in NP, i.e., is complexity-optimal. The obtained complexity bound is a result of dividing derivation rules in the algorithm into two sets: decomposition and equality rules, whose interplay yields derivation trees with branches of polynomial length with respect to the size of the investigated formula. We describe an implementation of the procedure and compare its performance with implementations of other calculi for SCI (for which, however, the termination results were not established). We show possible refinements of our algorithm and discuss the possibility of extending it to other non-Fregean logics.

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