Agi Kurucz
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View article: Deciding the Existence of Interpolants and Definitions in First-Order Modal Logic
Deciding the Existence of Interpolants and Definitions in First-Order Modal Logic Open
None of the first-order modal logics between $\mathsf{K}$ and $\mathsf{S5}$ under the constant domain semantics enjoys Craig interpolation or projective Beth definability, even in the language restricted to a single individual variable. It…
View article: On a Dependently Typed Encoding of Matching Logic
On a Dependently Typed Encoding of Matching Logic Open
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of match…
View article: From Interpolating Formulas to Separating Languages and Back Again
From Interpolating Formulas to Separating Languages and Back Again Open
Traditionally, research on Craig interpolation is concerned with (a) establishing the Craig interpolation property (CIP) of a logic saying that every valid implication in the logic has a Craig interpolant and (b) designing algorithms that …
View article: Unification in Matching Logic — Revisited
Unification in Matching Logic — Revisited Open
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
View article: The interpolant existence problem for weak K4 and difference logic
The interpolant existence problem for weak K4 and difference logic Open
As well known, weak K4 and the difference logic DL do not enjoy the Craig interpolation property. Our concern here is the problem of deciding whether any given implication does have an interpolant in these logics. We show that the nonexist…
View article: A non-uniform view of Craig interpolation in modal logics with linear frames
A non-uniform view of Craig interpolation in modal logics with linear frames Open
Normal modal logics extending the logic K4.3 of linear transitive frames are known to lack the Craig interpolation property, except some logics of bounded depth such as S5. We turn this `negative' fact into a research question and pursue a…
View article: Definitions and (Uniform) Interpolants in First-Order Modal Logic
Definitions and (Uniform) Interpolants in First-Order Modal Logic Open
We first consider two decidable fragments of quantified modal logic S5: the one-variable fragment and its extension S5ALC that combines S5 and the description logic ALC with the universal role. As neither of them enjoys Craig interpolation…
View article: Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic
Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic Open
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extr…
View article: Deciding the Existence of Interpolants and Definitions in First-Order Modal Logic
Deciding the Existence of Interpolants and Definitions in First-Order Modal Logic Open
None of the first-order modal logics between $\mathsf{K}$ and $\mathsf{S5}$ under the constant domain semantics enjoys Craig interpolation or projective Beth definability, even in the language restricted to a single individual variable. It…
View article: Deciding FO-rewritability of regular languages and ontology-mediated queries in Linear Temporal Logic
Deciding FO-rewritability of regular languages and ontology-mediated queries in Linear Temporal Logic Open
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extr…
View article: A tetrachotomy of ontology-mediated queries with a covering axiom
A tetrachotomy of ontology-mediated queries with a covering axiom Open
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based da…
View article: A Data Complexity and Rewritability Tetrachotomy of Ontology-Mediated Queries with a Covering Axiom
A Data Complexity and Rewritability Tetrachotomy of Ontology-Mediated Queries with a Covering Axiom Open
Aiming to understand the data complexity of answering conjunctive queries mediated by an axiom stating that a class is covered by the union of two other classes, we show that deciding their first-order rewritability is PSPACE-hard and obta…
View article: A tetrachotomy of ontology-mediated queries with a covering axiom
A tetrachotomy of ontology-mediated queries with a covering axiom Open
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based da…
View article: Horn Fragments of the Halpern-Shoham Interval Temporal Logic
Horn Fragments of the Halpern-Shoham Interval Temporal Logic Open
We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense),…
View article: Bimodal Logics with a “Weakly Connected” Component without the Finite Model Property
Bimodal Logics with a “Weakly Connected” Component without the Finite Model Property Open
There are two known general results on the finite model property (fmp) of\ncommutators [L,L'] (bimodal logics with commuting and confluent modalities). If\nL is finitely axiomatisable by modal formulas having universal Horn first-order\nco…
View article: The Decision Problem of Modal Product Logics with a Diagonal, and Faulty Counter Machines
The Decision Problem of Modal Product Logics with a Diagonal, and Faulty Counter Machines Open
In the propositional modal (and algebraic) treatment of two-variable\nfirst-order logic equality is modelled by a `diagonal' constant, interpreted in\nsquare products of universal frames as the identity (also known as the\n`diagonal') rela…