Comparing Calculi for First-Order Infinite-Valued Łukasiewicz Logic and First-Order Rational Pavelka Logic

Fragments of First - Order Logic over Infinite

We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for ω-languages: Σ2, ∆2, FO 2 ∩ Σ2 (and by duality FO 2 ∩ Π2), and FO . These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An im...

Extended Lambek Calculi and First-Order Linear Logic

In addition, though the syntax-semantics interface works for many of the standard examples, the Lambek calculus does not allow a non-peripheral quantifier to take wide scope (as we would need for sentence (1) below if we want the existential quantifier to have wide scope, the so-called “de re” reading) or nonperipheral extraction (as illustrated by sentence (2) below); see (Moortgat 2011, Secti...

First-Order Logic

Taming First-Order Logic

In this paper we define computationally well-behaved versions of classical first-order logic and prove that the validity problem is decidable1.

Extended First-Order Logic

We consider the EFO fragment of simple type theory, which restricts quantification and equality to base types but retains lambda abstractions and higher-order variables. We show that this fragment enjoys the characteristic properties of first-order logic: complete proof systems, compactness, and countable models. We obtain these results with an analytic tableau system and a concomitant model ex...