ML-1994-11: On One Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic

ML-1994-11: Alechina, Natasha (1994) On One Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic. [Report]

Abstract

On one decidable generalized quantifier logic corresponding to a decidable
fragment of first­order logic
Natasha Alechina

Van Lambalgen (1990) proposed a translation from a language containing a
generalized quantifier Q into a first­order language enriched with a family
of predicates R_i , for every arity i (or an infinitary predicate R) which
takes $Qx\phi(x, y_1, ..., y_n)$ to $\forall x (R(x, y_1, ..., y_n) \implies \phi(x, y_1, ..., y_n) )$ ($y_1, ..., y_n$ are precisely the free variables of
$Qx\phi$). The logic of Q (without ordinary quantifiers) corresponds therefore
to the fragment of first­order logic which contains only specially restricted
quantification. We prove that it is decidable using the method of semantic
tableaux. Similar results were obtained by Andreka and Nemeti (1994) using
the methods of algebraic logic.

Item Type: Report ML-1994-11 Mathematical Logic and Foundations (ML) 1994 12 Oct 2016 14:40 12 Oct 2016 14:40 https://eprints.illc.uva.nl/id/eprint/1357