On Inversion Principles

Moriconi, Enrico; Tesconi, Laura

doi:10.1080/01445340701830334

Cited by 24 publications

(8 citation statements)

References 10 publications

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“…Having accomplished that task, in this section we would like to briefly explore what we think is a promising way of expanding the proof-theoretic pluralist framework beyond MILP. 22 An important issue has remained in the background until now: the possibility of changing logic by changing the operational rules and by starting with a notion of derivability differing from the one we have chosen. This possibility is compatible with a proof-theoretic pluralism based on Belnap's global harmony.…”

Section: Families Of Harmonious Logicsmentioning

confidence: 99%

“…Pr. I, 2, 24b [20][21][22][23][24][25] Leaving exegetical details aside, it is interesting to note that in providing an informal gloss of the necessity feature of logical consequence, Beall and Restall themselves seem to have in mind something which echoes, at least at first glance, the thought expressed by Aristotle's passage. They write:…”

Section: Proof-theoretic Pluralism Meets Necessitymentioning

confidence: 99%

“…Many authors -e.g., Dummett[11], Read[28], and Steinberger[35] -criticize Belnap's definition because it is global: whether an operator is harmonious depends on the full set of rules of the calculus, and thus it might depend on the operational rules for other operators. These authors work mostly with natural deduction and present local explications of harmony that are usually based on so-called inversion principles, cf [22]…”

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Proof-theoretic pluralism

Ferrari

Orlandelli

2019

Synthese

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Starting from a proof-theoretic perspective, where meaning is determined by the inference rules governing logical operators, in this paper we primarily aim at developing a proof-theoretic alternative to the modeltheoretic meaning-invariant logical pluralism discussed in [1]. We will also outline how this framework can be easily extended to include a form of meaningvariant logical pluralism. In this respect, the framework developed in this paper -which we label two-level proof-theoretic pluralism -is much broader in scope than the one discussed in [1] L¬

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Section: Families Of Harmonious Logicsmentioning

confidence: 99%

Section: Proof-theoretic Pluralism Meets Necessitymentioning

confidence: 99%

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confidence: 99%

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Proof-theoretic pluralism

Ferrari

Orlandelli

2019

Synthese

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“…I establish his result proof-theoretically and constructively by means of normalisation inKürbis (2021), which can be read as a companion piece to the present paper. For the history of inversion principles, seeMoriconi and Tesconi (2008).6 It is an intuitionistic version of Parigot's classical system of free deduction when written in natural deduction style(Parigot 1992). The latter is a system of multiple conclusion sequent calculus.…”

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Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

Kürbis

2021

Synthese

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This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that deductions in normal form have the subformula property.

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“…satisfy the inversion principle: "A proof of the conclusion of an elimination is already 'contained' in the proofs of the premisses when the major premiss is inferred by introduction" (Prawitz, 1971, pp. 246-247, see also Lorenzen, 1955;Prawitz, 1965;Schroeder-Heister, 2007;Moriconi & Tesconi, 2008). The inversion principle suggests the idea that consecutive applications of the introduction rule followed immediately by the elimination rule constitute a redundancy.…”

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confidence: 99%

Harmonising Harmony

Tranchini¹

2015

The Review of Symbolic Logic

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The term 'harmony' refers to a condition that the rules governing a logical constant ought to satisfy in order to endow it with a proper meaning. Different characterizations of harmony have been proposed in the literature, some based on the inversion principle, others on normalization, others on conservativity. In this paper we discuss the prospects for showing how conservativity and normalization can be combined so to yield a criterion of harmony equivalent to the one based on the inversion principle: We conjecture that the rules for connectives obeying the inversion principle are conservative over normal deducibility. The plausibility of the conjecture depends in an essential way on how normality is characterized. In particular, a normal deduction should be understood as one which is irreducible, rather than as one which does not contain any maximal formula. We assume deducibility relations to hold between sets, rather than multi-sets of formulas.Otherwise, deducibility should be taken to be closed under contraction as well.

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On Inversion Principles

Cited by 24 publications

References 10 publications

Proof-theoretic pluralism

Proof-theoretic pluralism

Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules

Harmonising Harmony

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