Related papers: First-Order Modal Logic: Frame Definability and Li…

We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

This paper investigates first-order game logic and first-order modal mu-calculus, which extend their propositional modal logic counterparts with first-order modalities of interpreted effects such as variable assignments. Unlike in the…

Our main contributions can be divided in three parts: (1) Fixpoint extensions of first-order logic: we give a precise syntactic and semantic characterization of the relationship between $\mathrm{FO(TC^1)}$ and $\mathrm{FO(LFP)}$; (2)…

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…

In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of…

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…

Following the lines of the analysis done in [BPZ07, BCF07] for first-order G\"odel logics, we present an analogous investigation for Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order…

We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…

The language of modal logic is capable of expressing first-order conditions on Kripke frames. The classic result by Henrik Sahlqvist identifies a significant class of modal formulas for which first-order conditions -- or Sahlqvist…

Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…

First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…

We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…

We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt-Thomason Theorem and Fine's Canonicity Theorem for…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

Given a class $\mathcal C$ of models, a binary relation ${\mathcal R}$ between models, and a model-theoretic language $L$, we consider the modal logic and the modal algebra of the theory of $\mathcal C$ in $L$ where the modal operator is…

We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…