Related papers: An Abstract Approach to Consequence Relations
The pioneering work of Blok and J\'onsson and its further development by Galatos and Tsinakis initiated an abstract study of consequence relations using the tools of module theory, where consequence relations over all types of syntactic…
We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations - nowadays more commonly called multiple-conclusion logics - to the setting of non-deterministic matrices…
We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
In the present paper, we propose Abstract Algebraic Logic (AAL) as a general logical framework for Judgment Aggregation. Our main contribution is a generalization of Herzberg's algebraic approach to characterization results in on judgment…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…
These results are a contribution to the model theory of matrix consequence. We give a semantic characterization of uniform and couniform consequence relations. These properties have never been treated individually, at least in a semantic…
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue…
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…
In the present paper, we investigate consequence relations that are both paraconsistent and plausible (but still monotonic). More precisely, we put the focus on pivotal consequence relations, i.e. those relations that can be defined by a…
We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the \emph{use criterion}, according to which in order for some premises to have some…
We introduce a novel, logic-independent framework for the study of sequent-style proof systems, which covers a number of proof-theoretic formalisms and concrete proof systems that appear in the literature. In particular, we introduce a…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra.
This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning, and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of…