English
Related papers

Related papers: Many-valued coalgebraic logic over semi-primal var…

200 papers

We study generalized automata (in the sense of Ad\'amek-Trnkov\'a) in Joyal's category of (set-valued) combinatorial species, and as an important preliminary step, we study coalgebras for its derivative endofunctor $\partial$ and for the…

Category Theory · Mathematics 2026-01-14 Fosco Loregian

Formal multiple zeta values allow to study multiple zeta values by algebraic methods in a way that the open question about their transcendence is circumvented. In this note we show that Hoffman's basis conjecture for formal multiple zeta…

Number Theory · Mathematics 2024-06-21 Annika Burmester , Niclas Confurius , Ulf Kühn

In this paper, we introduce and investigate monadic NM-algebras: a variety of NM-algebras equipped with universal quantifiers. Also, we obtain some conditions under which monadic NM-algebras become monadic Boolean algebras. Besides, we show…

Logic · Mathematics 2017-09-15 Jun Tao Wang , Xiao Long Xin , Peng Fei He

We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii)…

Logic in Computer Science · Computer Science 2013-04-12 Daniel Gorín , Lutz Schröder

In this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal…

Logic · Mathematics 2022-04-18 Amanda Vidal

We study a coderivation from a cobimodule into a coalgebra. Vector cofields are defined by the action of a codual bicomodule on a coalgebra. This action is induced by a codifferential. A construction of a codual object in the category of…

Quantum Algebra · Mathematics 2009-10-31 A. Borowiec , G. A. Vazquez Coutino

We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…

Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…

Logic in Computer Science · Computer Science 2024-11-26 Victoria Vollmer , Danielle Marshall , Harley Eades , Dominic Orchard

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. We investigate the structure properties of the endomorphism algebras of semi-tilting $A$-modules, and prove that the endomorphism algebras arising from the…

Representation Theory · Mathematics 2015-03-19 Shunhua Zhang

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…

Logic · Mathematics 2024-06-25 Wesley H. Holliday

In the present paper, we endow the logics of topological quasi Boolean algebras, topological quasi Boolean algebras 5, intermediate algebras of types 1-3, and pre-rough algebras with proper multi-type display calculi which are sound,…

Logic · Mathematics 2018-08-23 Giuseppe Greco , Fei Liang , Krishna Manoorkar , Alessandra Palmigiano

We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…

Logic · Mathematics 2026-02-12 Tumadhir Alsulami , Marcel Jackson

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…

Logic in Computer Science · Computer Science 2007-05-23 Pavel Naumov

The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…

Logic in Computer Science · Computer Science 2011-03-04 Zoran Majkic

We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In…

Logic · Mathematics 2025-01-17 Amir Farahmand Parsa , Meghdad Ghari

We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…

Logic in Computer Science · Computer Science 2020-04-28 Cameron Calk , Anupam Das , Tim Waring

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…

Rings and Algebras · Mathematics 2015-03-25 L. M. Cabrer , H. A. Priestley

In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…

Formal Languages and Automata Theory · Computer Science 2020-01-13 Dan Shiebler , Alexis Toumi , Mehrnoosh Sadrzadeh

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

Representation Theory · Mathematics 2020-06-09 Sibylle Schroll , Hipolito Treffinger

Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired…

Category Theory · Mathematics 2020-01-15 Thorsten Wißmann , Stefan Milius , Shin-ya Katsumata , Jérémy Dubut