Related papers: Representation theory of logics: a categorial appr…

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…

We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…

In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…

Motivated by applications in modelling quantum systems using coalgebraic techniques, we introduce a fibred coalgebraic logic. Our approach extends the conventional predicate lifting semantics with additional modalities relating conditions…

This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…

This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…

A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…

We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…

The draft paper defines a system, which is capable of maintaining bases of test cases for logical specifications. The specifications, which are subject to this system are transformed from their original shape in first-order logic to…

Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

Subtyping, also known as subtype polymorphism, is a concept extensively studied in programming language theory, delineating the substitutability relation among datatypes. This property ensures that programs designed for supertype objects…

We introduce a proper multi-type display calculus for bilattice logic (with conflation) for which we prove soundness, completeness, conservativity, standard subformula property and cut-elimination. Our proposal builds on the product…

Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…

This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…

Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…

Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…

Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…

In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to…