We solve a problem of Friedman by showing the existence of a logic stronger than first-order logic even for countable models, but still satisfying the general compactness theorem, assuming e.g. the ...

We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as ...

if ``0 < ε ≤ ...

ABSTRACT: Adopting a different method from the previous scholars, this article deduces the remaining 23 valid syllogisms just taking the syllogism AEE-4 as the basic axiom. The basic idea of this ...

A doubly-quantified sentence like 'Every bear approached a tent is ambiguous': Did every bear approach a different tent, or did they approach the same tent? These two interpretations are assumed to be ...

In order to provide a consistent explanation for Aristotelian modal syllogistic, this paper reveals the reductions between the Aristotelian modal syllogism I A I-3 and the other valid modal syllogisms ...