Related papers: Congruence Filter Pairs, Adjoints and Leibniz Hier…
We adjust the notion of finitary filter pair, which was coined for creating and analyzing finitary logics, in such a way that we can treat logics of cardinality $\kappa$, where $\kappa$ is a regular cardinal. The corresponding new notion is…
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…
We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…
A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz…
We study properties that allow first-order theories to be disjointly combined, including stable infiniteness, shininess, strong politeness, and gentleness. Specifically, we describe a Galois connection between sets of decidable theories,…
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.…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic…
We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…
Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…
We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For $m>0$, let $\mathrm{L}_m$ be the logic defined by axiom $\lozenge^{m+1} p\to \lozenge p\vee p$. We construct filtrations for…
A profile describes a set of properties, e.g. a set of skills a person may have, a set of skills required for a particular job, or a set of abilities a football player may have with respect to a particular team strategy. Profile matching…
The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…
In this paper, we study the congruences, prime filters and prime ideals of horizontal sums of bounded lattices, then, through a construction based on horizontal sums and without enforcing the Continuum Hypothesis, we are modifying an…
Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…
We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is…
Let $\mathbf{F}=\left\langle F,R\right\rangle $ be a finite Kripke frame. A congruence of $\mathbf{F}$ is a bisimulation of $\mathbf{F}$ that is also an equivalence relation on F. The set of all congruences of $\mathbf{F}$ is a lattice…