Related papers: Hierarchies in inclusion logic with lax semantics

We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…

Ellipses are a meta-linguistic notation for denoting terms the size of which are specified by a meta-variable that ranges over the natural numbers. In this work, we present a systematic approach for encoding such meta-expressions in the…

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are…

In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence…

Inquisitive team logic is a variant of inquisitive logic interpreted in team semantics, which has been argued to provide a natural setting for the regimentation of dependence claims. With respect to sentences, this logic is known to be…

The terms 'semantics' and 'ontology' are increasingly appearing together with 'explanation', not only in the scientific literature, but also in organizational communication. However, all of these terms are also being significantly…

Team Semantics generalizes Tarski's Semantics for First Order Logic by allowing formulas to be satisfied or not satisfied by sets of assignments rather than by single assignments. Because of this, in Team Semantics it is possible to extend…

Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete…

The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…

This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.

The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engstr\"om, comparing them with a more general, higher-order definition of team quantifier. We show that…

Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current large-scale reasoning models primarily rely on scaling up training datasets with diverse…

Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…

Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…

We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem.…

We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…

We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…

Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…