HYPE: A System of Hyperintensional Logic (with an Application to Semantic Paradoxes).
This article introduces, studies, and applies a new system of logic which is called 'HYPE'. In HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth value gluts (overdeterminedness). Simple and natural semantic rules for negation and the conditional operator...
| Publicado en: | Journal of Philosophical Logic Vol. 48; no. 2; pp. 305 - 406 |
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| Formato: | Artículo |
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Springer Nature
Apr2019
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=135326429&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 135326429 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Apr2019 vid: 48 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 135326429 10.1007/s10992-018-9467-0 ppf: 305 ppct: 101 formats: fmt: @attributes: type: P size: 2.1MB tig: atl: HYPE: A System of Hyperintensional Logic (with an Application to Semantic Paradoxes). aug: au: Leitgeb, Hannes affil: LMU Munich, Geschwister-Scholl-Platz 1, 80539, Munich, Germany su: Truth functions (Mathematical logic) Semantics Finite model theory Graph theory Combinatorics sug: subj: Truth functions (Mathematical logic) Semantics Finite model theory Graph theory Combinatorics keyword: Clutters Hyperintensional Intuitionistic logic Paraconsistent logic Semantic paradoxes Truthmaker semantics ab: This article introduces, studies, and applies a new system of logic which is called 'HYPE'. In HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth value gluts (overdeterminedness). Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE's logical connectives. Furthermore, HYPE's first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2019. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2019 holdings: @attributes: islocal: N |
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