A Canonical Model for Constant Domain Basic First-Order Logic

Middleton, Ben

doi:10.1007/s11225-020-09900-7

Cited by 1 publication

(6 citation statements)

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“…The next lemma supercedes Lemma 7 in [9], which unnecessarily appealed to Relative Deduction. 10 Lemma 10 (Relative Extension).…”

Section: The Canonical Model the Canonical Model For Bql Rmentioning

confidence: 81%

“…φ i is a possibly discharged assumption in the right main subtree of an application of modus ponens). So, for example, the occurrence of α → ( → ) in each of the 4 See [9] for a discussion of BQL CD . 5 The variable domain extension of Visser's basic propositional logic was studied by Ruitenburg [13] under the name 'basic predicate calculus'.…”

Section: Tjk D +mentioning

confidence: 99%

“…Hence Γ 0 ⊢ TJK d + φ. 9 TJK + , first studied in [1], is the logic obtained by removing ∃-Elim from the original axiomatization of TJK d + . Write Γ ⊢ TJK + φ iff there exists a proof of φ from Γ in TJK + .…”

Section: Bql Rmentioning

confidence: 99%

“…CD is identical to the canonical model for BQL CD (defined in [9]). I repeat the definition here for ease of reference.…”

Section: The Canonical Model the Canonical Model For Bql Rmentioning

confidence: 99%

“…This notation derives from the fact that N BQL CD is sound and complete with respect to BQL CD (see[9] and §5.1 of this paper, where part of the proof in[9] is simplified).…”

mentioning

confidence: 99%

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Binary Kripke Semantics for a Strong Logic for Naive Truth

Middleton¹

2020

The Review of Symbolic Logic

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I show that the logic $\textsf {TJK}^{d+}$ , one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by (i) dropping the requirement that the accessibility relation is reflexive and (ii) only allowing reflexive worlds to serve as counterexamples to logical consequence. In addition, I provide a simplified natural deduction system for $\textsf {TJK}^{d+}$ , in which a restricted form of conditional proof is used to establish conditionals.

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“…The next lemma supercedes Lemma 7 in [9], which unnecessarily appealed to Relative Deduction. 10 Lemma 10 (Relative Extension).…”

Section: The Canonical Model the Canonical Model For Bql Rmentioning

confidence: 81%

Section: Tjk D +mentioning

confidence: 99%

Section: Bql Rmentioning

confidence: 99%

“…CD is identical to the canonical model for BQL CD (defined in [9]). I repeat the definition here for ease of reference.…”

Section: The Canonical Model the Canonical Model For Bql Rmentioning

confidence: 99%

“…This notation derives from the fact that N BQL CD is sound and complete with respect to BQL CD (see[9] and §5.1 of this paper, where part of the proof in[9] is simplified).…”

mentioning

confidence: 99%

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