A Bounded Translation of Intuitionistic Propositional Logic into Basic Propositional Logic

Aghaei, Mojtaba; Ardeshir, Mohammad

doi:10.1002/(sici)1521-3870(200005)46:2<199::aid-malq199>3.0.co;2-b

Cited by 8 publications

(3 citation statements)

References 3 publications

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“…There are some interesting problems for future work. It is already known that intuitionistic logic is embedded into basic propositional logic by a bounded translation [31]. Using the sequent calculus G4ip for intuitionistic logic (cf.…”

Section: Fundingmentioning

confidence: 99%

Residuated Basic Logic

Lin,

2023

Axioms

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Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL, which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable.

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Section: Fundingmentioning

confidence: 99%

Residuated Basic Logic

Lin,

2023

Axioms

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“…Ardeshir's translation is comparable to Gödel's negative translation, which embeds Classical Logic in the Intuitionistic Logic. A strict upper bound of the translation from Intuitionistic Logic into Basic Logic, when it is restricted to the propositional case, was introduced in (Aghaei & Ardeshir, 2000). Ardeshir's latest v contribution to this area, (Ardeshir & Vaezian, 2012), was to introduce a logic, called U, which is weaker than both Visser's Basic Logic (Visser, 1981) and Sambin's Basic Logic (Battilotti & Sambin, 1999).…”

Section: Prefacementioning

confidence: 99%

Mathematics, Logic, and their Philosophies

Mojtahedi¹,

Rahman²,

Zarepour³

2021

Logic, Epistemology, and the Unity of Science

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Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal frameworks, for example, constructive type theory, deontic logics, dialogical logics, epistemic logics, modal logics, and proof-theoretical semantics, have the potential to cast new light on basic issues in the discussion of the unity of science.This series provides a venue where philosophers and logicians can apply specific systematic and historic insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity.

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“…Basic Propositional Logic was first introduced by Visser [26] 1) and was extended to Basic Predicate Calculus by Ruitenburg [17]. "It is the sub-logic of the intuitionistic logic which is characterized by the class of Kripke frames with transitive (but not necessarily reflexive) accessibility relations, so that the modal logic K4 corresponds to this logic by Gödel translation of the intuitionistic logic into the modal logic S4.…”

Section: Introductionmentioning

confidence: 99%

Provably total functions of Basic Arithmetic

Salehi

2003

Mathematical Logic Qtrly

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It is shown that all the provably total functions of Basic Arithmetic BA, a theory introduced by Ruitenburg based on Predicate Basic Calculus, are primitive recursive. Along the proof a new kind of primitive recursive realizability to which BA is sound, is introduced. This realizability is similar to Kleene's recursive realizability, except that recursive functions are restricted to primitive recursives.

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A Bounded Translation of Intuitionistic Propositional Logic into Basic Propositional Logic

Cited by 8 publications

References 3 publications

Residuated Basic Logic

Residuated Basic Logic

Mathematics, Logic, and their Philosophies

Provably total functions of Basic Arithmetic

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