Year: 2025
Type: article
Abstract: In this paper, we explore the possibility of constructing algebra-valued models for connexive set theories. In particular, we build an algebra-valued model on top of the four-element lattice $$\mathbb{M}\mathbb{C}$$ M C which semantically captures Wansing’s logic of material connexvity (MC). We show that the resulting model validates an axiom system that is classically equivalent to $$\textsf{ZF}$$ ZF and that its underlying logic is a connexive logic. For this purpose, we tweak our semantic interpretation of set-membership and identity resulting in a model with a classical notion of identity and a non-classical notion of set-membership. Finally, in the conclusion, we discuss the role of our model within the ongoing debate between logical pluralism and monism.
Source: Studia Logica
Author: Santiago Jockwich Martinez
Institution: University of Oslo
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funder: Universitetet i Oslo
OpenAlex ID: W4410128829