Related papers: From Interpolating Formulas to Separating Language…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
We complete Maksimova's classification of the normal extensions of S4 with interpolation. In particular, we prove Craig interpolation for the six extensions of S4 for which Craig interpolation was still open. The proof strategy builds upon…
Interoperability is the ability of a programming language to work with systems based on different languages and paradigms. These days, many widely used high-level language impementations provide access to external functionalities. In this…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…
Concurrent Constraint Programming (CCP) is a simple and powerful model for concurrency where agents interact by telling and asking constraints. Since their inception, CCP-languages have been designed for having a strong connection to logic.…
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated…
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…
Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…
We introduce and investigate the notion of uniform Lyndon interpolation property (ULIP) which is a strengthening of both uniform interpolation property and Lyndon interpolation property. We prove several propositional modal logics including…
We show that the guarded-negation fragment is, in a precise sense, the smallest extension of the guarded fragment with Craig interpolation. In contrast, we show that full first-order logic is the smallest extension of both the two-variable…
We develop a Gentzen-style proof theory for super-Belnap logics (extensions of the four-valued Dunn-Belnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood…
There are exactly two maximal schematic extensions of the relevant logic R with the variable sharing property. We establish that one of them has a strong form of interpolation for deducibility, thereby giving an example of a well-known…
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…
Lexical semantic typology has identified important cross-linguistic generalizations about the variation and commonalities in polysemy patterns---how languages package up meanings into words. Recent computational research has enabled…