This is a preview. Log in through your library . Abstract This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the ...

We give a completeness theorem for a logic with probability quantifiers which is equivalent to the logics described in a recent survey paper of Keisler [K]. This result improves on the completeness ...

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 ...

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 ...

The study of monadic algebraic structures and fuzzy logic has evolved into a vibrant research area that bridges abstract algebra with the nuanced reasoning of uncertainty. By incorporating unary ...

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 ...

Originally published on Sept. 25, 2018. In a world of divisive politics, rhetoric and debate, author Eugenia Cheng has the secret to winning an argument: mathematical logic. Cheng, a mathematician and ...

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 ...