Related papers: Lindenbaum-type Logical Structures
We find an order-theoretic characterization of the Lindenbaum algebra of intuitionistic propositional logic in n variables.
Lindstr\"om theorems characterize logics in terms of model-theoretic conditions such as Compactness and the L\"owenheim-Skolem property. Most existing characterizations of this kind concern extensions of first-order logic. But on the other…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
During his brief life, the Polish mathematician and logician Adolf Lindenbaum (1904--1941) contributed to mathematical logic, among other things, by several significant achievements. Some results of Lindenbaum's, which bear his name, were…
We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structural logic: we prove that AECs with intersections correspond…
In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
A logic family is a bunch of logics that belong together in some way. First-order logic is one of the examples. Logics organized into a structure occurs in abstract model theory, institution theory and in algebraic logic. Logic families…
We extend the main result of (G. Badia and G. Olkhovikov. A Lindstr\"om theorem for intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 61 (1): 11--30 (2020)) to the first-order intuitionistic logic (with and without…
We ask, when is a property of a model a logical property? According to the so-called Tarski-Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
In 1969, Per Lindstrom proved his celebrated theorem characterising the first-order logic and established criteria for the first-order definability of formal theories for discrete structures. K. J. Barwise, S. Shelah, J. Vaananen and others…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
In the style of Lindstr\"om's theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive power) abstract logic satisfying a certain form of…
Lindstr\"om's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward L\"owenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious…
The aim of this work is to provide a special kind of conservative translation between abstract logics, namely an \textit{abstract Glivenko's theorem}. Firstly we define institutions on the categories of logic, algebraizable logics, and…
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…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…