Related papers: Covering and separation for logical fragments with…
The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Word segmentation stands as a cornerstone of Natural Language Processing (NLP). Based on the concept of "comprehend first, segment later", we propose a new framework to explore the limit of unsupervised word segmentation with Large Language…
We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Foundation models, such as Large language Models (LLMs), have attracted significant amount of interest due to their large number of applications. However, when handling tasks involving repetitive sub-tasks and/or deceptive contents, such as…
Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison $x<y$ and predicates for $x \equiv i \mod n$ has been investigated by Barrington, Compton,…