Intermediate logics in the setting of team semantics

TL;DR

This paper explores alternative methods to define intermediate logics within team semantics by modifying tIPC with different disjunctions, providing characterization and generalized semantics.

Contribution

It introduces two new approaches to intermediate logics in team semantics, expanding the theoretical framework with axiomatic modifications and generalized semantics.

Findings

Characterization theorem for the first approach

Introduction of generalized team semantics in the second approach

Comparison of local and global disjunctions in team semantics

Abstract

Several authors have recently defined intuitionistic logic based on team semantics (tIPC). In this paper we provide two alternative approaches to intermediate logics in the team semantics setting. We do this by modifying tIPC with axioms written with two different versions of disjunction in the logic, a local one and global one. We prove a characterization theorem in the first approach and we introduce a generalized team semantics in the second one.