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Dal superamento del riduzionismo insiemistico alla ricerca di una più ampia e profonda comprensione tra matematici e studiosi di altre discipline scientifiche ed umanistiche

Ennio De Giorgi (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Proponiamo in questa Nota un quadro assiomatico aperto e non riduzionista, che si basa sulle idee primitive di qualità e relazione, in cui speriamo sia possibile innestare i concetti fondamentali della Matematica, della Logica e dell’Informatica (di cui diamo solo alcuni primissimi esempi). Auspichiamo che sviluppando liberamente tale quadro sia possibile giungere ad un fruttuoso confronto critico delle idee fondamentali delle diverse discipline scientifiche ed umanistiche, non ristretto agli «specialisti...

Decidability and definability results related to the elementary theory of ordinal multiplication

Alexis Bès (2002)

Fundamenta Mathematicae

The elementary theory of ⟨α;×⟩, where α is an ordinal and × denotes ordinal multiplication, is decidable if and only if α < ω ω . Moreover if | r and | l respectively denote the right- and left-hand divisibility relation, we show that Th ⟨ ω ω ξ ; | r ⟩ and Th ⟨ ω ξ ; | l ⟩ are decidable for every ordinal ξ. Further related definability results are also presented.

Deciding inclusion of set constants over infinite non-strict data structures

Manfred Schmidt-Schauss, David Sabel, Marko Schütz (2007)

RAIRO - Theoretical Informatics and Applications

Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are non-strict. This...

Deciding whether a relation defined in Presburger logic can be defined in weaker logics

Christian Choffrut (2008)

RAIRO - Theoretical Informatics and Applications

We consider logics on ℤ and ℕ which are weaker than Presburger arithmetic and we settle the following decision problem: given a k-ary relation on ℤ and ℕ which are first order definable in Presburger arithmetic, are they definable in these weaker logics? These logics, intuitively, are obtained by considering modulo and threshold counting predicates for differences of two variables.

Decision problems among the main subfamilies of rational relations

Olivier Carton, Christian Choffrut, Serge Grigorieff (2006)

RAIRO - Theoretical Informatics and Applications

We consider the four families of recognizable, synchronous, deterministic rational and rational subsets of a direct product of free monoids. They form a strict hierarchy and we investigate the following decision problem: given a relation in one of the families, does it belong to a smaller family? We settle the problem entirely when all monoids have a unique generator and fill some gaps in the general case. In particular, adapting a proof of Stearns, we show that it is recursively decidable whether...

Declarative and procedural semantics of fuzzy similarity based unification

Peter Vojtáš (2000)

Kybernetika

In this paper we argue that for fuzzy unification we need a procedural and declarative semantics (as opposed to the two valued case, where declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in narrow sense. We base our semantics on a formal model of fuzzy logic programming extended...

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