Model-Theoretic Inferentialism; Paraconsistency; Categoricity

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Jafari Javid; Hosseini Davood

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Journal Paper

Paper Information

Journal: Ayeneh Ma‘refat Year:2024 | Volume:24 | Issue:2 Page(s): 52-68

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Information Journal Paper

Title

Model-Theoretic Inferentialism; Paraconsistency; Categoricity

Author(s)

Jafari Javid | Hosseini Davood | Issue Writer Certificate

Keywords

model-theoretic inferentialismQ4

paraconsistencyQ4

categoricityQ4

Abstract

According to model-theoretic inferentialism (and despite proof-theoretic semantics and model-theoretic semantics), both proof-theoretic and model-theoretic notions play a role in the meaning of logical constants. However, proof-theoretic notions have a more fundamental role compared to model-theoretic notions, so that the semantics and its structure are determined by the proof-theoretic notions. In other words, in proof-theoretic inferentialism, we follow a method by which we can read the semantics from the proof theory. This approach is related to the problem of categoricity and Carnap's non-normal models for proof systems. In this paper we investigate this issue for two paraconsistent logics, mbC and LP. We show that while multi-succedent sequent calculi are categorical for mbC, they are not for LP. That latter has non-normal models. We argue that for the latter we cannot easily read the semantics from the proof theory, except at the cost of distorting the notion of logical consequence.

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