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This research aims to advance bilateral proof-theoretic semantics by defining both proofs and refutations as foundational elements.

Bilateral Base-extension Semantics

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This research aims to advance bilateral proof-theoretic semantics by defining both proofs and refutations as foundational elements.
Develop a bilateral version of base-extension semantics incorporating atomic proof and refutation rules.
Establish soundness and completeness concerning bi-intuitionistic logic.
Define duality notions for atomic rules to derive bilateral semantic harmony results.
Bilateral semantic harmony is confirmed as a restatement of the syntactic horizontal inversion principle.
Established embeddings between different language fragments through atomic bases.
Demonstrated preservation of harmony notions within the core semantics through inferences.

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Randomized trial explores proof-theoretic semantics, enhancing logical frameworks through bilateralism.

Barroso-Nascimento et al. (2026) studied this question.

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