The de Jongh property for Basic Arithmetic

Ardeshir, Mohammad; Mojtahedi, S. Mojtaba

doi:10.1007/s00153-014-0394-7

Cited by 9 publications

(3 citation statements)

References 12 publications

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“…It is proved by (de Jongh, 1970) that the propositional logic of HA is Intuitionistic Logic. In the same vein, it is shown by (Ardeshir & Mojtahedi, 2014) that the propositional logic of BA is Basic Logic.…”

Section: Prefacementioning

confidence: 92%

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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Section: Prefacementioning

confidence: 92%

Mathematics, Logic, and their Philosophies

Mojtahedi¹,

Rahman²,

Zarepour³

2021

Logic, Epistemology, and the Unity of Science

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“…This is the semantic form of the arithmetized completeness theorem [31, Theorem 6.10] together with the Σ 0 -elementary canonical embedding obtained in Remark 4.4. This theorem is also referred to as the interpretability theorem (see, e.g., [2,21]). We will digest the proof of the relativized form of this theorem in Appendix B.…”

Section: Remark 32 Let I = (I ≤ I M ) Be An Iqc-kripke Model With A...mentioning

confidence: 99%

Extended Frames and Separations of Logical Principles

Fujiwara¹,

Ishihara²,

Nemoto³

et al. 2023

Bull. symb. log

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We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$ . To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$ . We see several examples which give us separations among omniscience principles.

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“…De Jongh, Verbrugge and Visser [7] introduced the de Jongh property and showedamong other results-that L(HA(J)) = J for logics J that are characterised by classes of finite frames. Considering a logic that is weaker than intuitionistic logic, Ardeshir and Mojtahedi [2] proved that the propositional logic of basic arithmetic is the basic propositional calculus.…”

Section: Logics and The De Jongh Propertymentioning

confidence: 99%