arXiv subjects

Ryo Takemura

Publications and source records attributed to Ryo Takemura.

2 recordsLinked to original sources

arXiv2025

A completeness theorem in proof-theoretic semantics via set-theoretic semantics

We investigate the completeness of intuitionistic logic with respect to Prawitz's proof-theoretic validity. As an intuitionistic natural deduction system, we apply atomic second-order intuitionistic propositional logic. By developing phase semantics with proof-terms introduced by Okada & Takemura (2007), we construct a special phase model whose domain consists of closed terms. We then discuss how our phase semantics can be regarded as proof-theoretic semantics, and we prove completeness with respect to proof-theoretic semantics via our phase semantics.

math.LO↗

arXiv2015

Euler diagrams as an introduction to set-theoretical models

Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an introduction to set-theoretical models. We show that the model-theoretic notions of validity and invalidity are characterized by Euler diagrams, and, in particular, that model construction can be described as a manipulation of Euler diagrams.

cs.CY↗