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Binding Forms in First-Order Logic

Authors Fabio Mogavero, Giuseppe Perelli

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Fabio Mogavero
Giuseppe Perelli

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Fabio Mogavero and Giuseppe Perelli. Binding Forms in First-Order Logic. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 648-665, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CSL.2015.648

Abstract

Aiming to pinpoint the reasons behind the decidability of some complex extensions of modal logic, we propose a new classification criterion for sentences of first-order logic, which is based on the kind of binding forms admitted in their expressions, i.e., on the way the arguments of a relation can be bound to a variable. In particular, we describe a hierarchy of four fragments focused on the Boolean combinations of these forms, showing that the less expressive one is already incomparable with several first-order limitations proposed in the literature, as the guarded and unary negation fragments. We also prove, via a novel model-theoretic technique, that our logic enjoys the finite-model property, Craig's interpolation, and Beth's definability. Furthermore, the associated model-checking and satisfiability problems are solvable in PTime and Sigma_3^P, respectively.
Keywords
  • First-Order Logic
  • Decidable Fragments
  • Satisfiability
  • Model Checking

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