Neutral Free Logic: Motivation, Proof Theory and Models.
Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka The Journal of Philosophy, 56, 125–137 1959; Lambert Notre Dame Journal of Formal Logic, 8, 133–144 1967, 1997, 2001). What those assumptions are varies, bu...
| Publicado en: | Journal of Philosophical Logic Vol. 52; no. 2; pp. 519 - 555 |
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| Autores principales: | , |
| Formato: | Artículo |
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Springer Nature
Apr2023
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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=162802439&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 162802439 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: Apr2023 vid: 52 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 162802439 10.1007/s10992-022-09679-z ppf: 519 ppct: 36 formats: fmt: @attributes: type: P size: 806KB tig: atl: Neutral Free Logic: Motivation, Proof Theory and Models. aug: au: Pavlović, Edi Gratzl, Norbert affil: Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft Munich Center for Mathematical Philosophy (MCMP), Ludwig-Maximilians Universität München, Geschwister Scholl Platz 1, 80539, München, Germany su: Proof theory Model theory First-order logic Presupposition (Logic) Logic Motivation (Psychology) sug: subj: Proof theory Model theory First-order logic Presupposition (Logic) Logic Motivation (Psychology) keyword: Cut elimination G3 sequent calculus Generalized semantics Neutral free logic ab: Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka The Journal of Philosophy, 56, 125–137 1959; Lambert Notre Dame Journal of Formal Logic, 8, 133–144 1967, 1997, 2001). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free logics reject the claim that names need to denote in (ii). Positive free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, negative free logic treats them as uniformly false, and neutral free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (Bulletin of the Section of Logic, 48(2), 137–158 2019) as well as classical logic in Pavlović and Gratzl (Journal of Philosophical Logic, 50, 117–148 2021), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (Studia Logica, 105(1), 93–119 2017, Journal of Applied Non-Classical Logics, 30(3), 272–289 2020), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2023. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2023 holdings: @attributes: islocal: N |
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