相关论文: An implication in orthologic
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Propositional logic serves as a fundamental cornerstone in mathematical logic. This paper delves into a semiring characterization of propositional logic, employing the Gr\"oebner-Shirshov basis theory to furnish an algebraic framework for…
Injectivity of objects with respect to a set $\ch$ of morphisms is an important concept of algebra, model theory and homotopy theory. Here we study the logic of injectivity consequences of $\ch$, by which we understand morphisms $h$ such…
Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for…
We deal with equations over free semilattice of infinite rank and prove that any infinite consistent system of equations is equivalent to its finite subsystem. Moreover, we describe irreducible algebraic sets and solve some algorithmic…
We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models and, hence, the results apply to a wide class of modal logics including, for example,…
We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based…
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…
Hemi-implicative semilattices (lattices), originally defined under the name of weak implicative semilattices (lattices), were introduced by the second author of the present paper. A hemi-implicative semilattice is an algebra…
Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary…
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…
We introduce maximal and average coherence on lattices by analogy with these notions on frames in Euclidean spaces. Lattices with low coherence can be of interest in signal processing, whereas lattices with high orthogonality defect are of…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
We prove undecidability for every positive relevant logic extending the system axiomatized by hypothetical syllogism, prefixing, and suffixing and contained in the logic of the semilattice frame $(P_{\mathrm{fin}}(\mathbb{N}), \cup,…
We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.
We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. The validity of the various distributivity laws is studied and forms the basis for a comparison…