We have seen that the language of propositional logic allows us to build up expressions from propositional variables A, B, C, \ldots using propositional connectives like \to, \wedge, \vee, and \neg.

In this chapter, you will learn how to write proofs in Lean. We will start with a purely mechanical translation that will enable you to represent any natural deduction proof in Lean. We will see, ...

Large Language Models (LLMs) have made significant strides in various Natural Language Processing tasks, yet they still struggle with mathematics and complex logical reasoning. Chain-of-Thought (CoT) ...

Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normalform theorems. On the basis of these ...

Synthese, Vol. 125, No. 1/2, Festschrift in Honor of Newton C. A. Da Costa on the Occasion of His Seventieth Birthday (Oct. - Nov., 2000), pp. 147-154 (8 pages) In this note, we outline a definition ...

Abstract: The report explores the problem of developing a common base of mathematical support for the problem of modeling control systems for objects of great complexity. The problem of reconstructing ...

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

Computational complexity and proof systems are fundamental areas in theoretical computer science that explore the limits of what can be computed and how efficiently problems can be solved. Recent ...