In discrete mathematics, predicates and quantifiers are fundamental concepts that allow us to express statements about sets, elements, and their relationships in a formal and logical manner. These ...

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 ...

Abstract: We study the existence of Hanf normal forms for extensions FO(Q) of first-order logic by sets Q ⊆ P(ℕ) of unary counting quantifiers. A formula is in Hanf normal form if it is a Boolean ...

Abstract: Logical reasoning of text requires neural models to possess strong contextual comprehension and logical reasoning ability to draw conclusions from limited information. To improve the logical ...

ABSTRACT: 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 ...