Problem
Research questions and friction points this paper is trying to address.
proof-theoretic semantics
inference-behaviour semantics
multi-dimensional sequent calculus
automated reasoning
many-valued logics
Towards Automated Proof-Theoretic Semantics: Inference-Behaviour Semantics for 3-Dimensional K3 and LP
🤖 AI Summary
This work addresses the proof-theoretic semantic modeling of connectives in many-valued logics by proposing a unified approach based on inferential behavior semantics (I-bS). It extends I-bS for the first time to a three-dimensional sequent calculus framework, thereby constructing formal semantic models for both Kleene’s three-valued logic K3 and Priest’s logic LP. The paper rigorously establishes that these two logics share identical connective semantics and are conservative extensions of the classical sequent system LK. Beyond revealing a deep proof-theoretic connection between K3 and LP, this study advances the MUltlog system’s capacity to support automated proof-theoretic semantics for many-valued logics, laying a theoretical foundation for future developments in automated reasoning tools.
📝 Abstract
Inference-behaviour Semantics (I-bS) is a sequent calculus-based substructural approach to proof-theoretic semantics (P-tS), focussed on modelling the relationships of connective meanings across different logics. This paper provides a case study of how I-bS can be extended to any finitely multi-dimensional sequent calculus. To this end, we give I-bS for the 3-dimensional sequent calculi K3 (Strong Kleene) and LP (Logic of Paradox). We find that the K3 and LP connectives have the same meaning and that their meaning conservatively extends the meaning of the corresponding classical LK connectives. We situate this result within the wider project of integrating I-bS with MUltlog. The goal is to automate the generation of I-bS for arbitrary multi-valued logics using a MUltlog-style system, thus contributing towards the computational automation of P-tS approaches.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Inference-behaviour Semantics
sequent calculus
multi-dimensional logic
proof-theoretic semantics
automated semantics generation
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