Classical Logic as Intuitionistic Logic with Duality
read the original abstract
The field of proof-theoretic semantics (P-tS) offers an alternative approach to meaning in logic that is based on inference and argument (rather than truth in a model). It has been successfully developed for various logics; in particular, Sandqvist has developed such semantics for both classical and intuitionistic logic. In the case of classical logic, P-tS provides a conception of consequence that avoids an a priori commitment to the principle of bivalence, addressing what Dummett identified as a significant foundational challenge in logic. In this paper, we propose an alternative P-tS for classical logic, which essentially extends the P-tS for intuitionistic logic by operating over literals rather than atomic propositions. Importantly, literals are atomic and not defined by negation but are related by a primitive duality encoded inferentially at the atomic level. This semantics illustrates the perspective that classical logic can be understood as intuitionistic logic supplemented by a principle of duality, offering fresh insights into the relationship between these two systems.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Towards an Inferentialist Account of Information Through Proof-theoretic Semantics
An inferentialist account of information is outlined using proof-theoretic semantics to introduce the inferon and model inference-based information flow in distributed systems.
-
Towards an Inferentialist Account of Information Through Proof-theoretic Semantics
Outlines first steps toward an inferentialist theory of information by adapting Dretske via inferability, realizing it with proof-theoretic semantics to define the 'inferon', and applying the framework to distributed ...
-
Towards an Inferentialist Account of Information Through Proof-theoretic Semantics
Authors propose replacing truth with inferability in Dretske's information concepts and use proof-theoretic semantics to develop an inferentialist primitive 'inferon' for modeling information in distributed systems.
-
Towards an Inferentialist Account of Information Through Proof-theoretic Semantics
An inferentialist theory of information is outlined by adapting proof-theoretic semantics to replace truth-based accounts, introducing the 'inferon' and applying it to information flow in distributed systems.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.