Some Comments on Ian Rumfitt’s Bilateralism

Kürbis, Nils

doi:10.1007/s10992-016-9395-9

Cited by 18 publications

(28 citation statements)

References 8 publications

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“…It should be possible to adapt this and the present work to bilateral formulations of such logics. 5 The account also rules out the bilateral intuitionistic logic proposed by the author [13]: its rules are not harmonious according to it. I argued that the system satisfies all the requirements Rumfitt imposes on a satisfactory bilateral logic; and so it does.…”

Section: Introductionmentioning

confidence: 80%

“…According to Dummett, the rules governing a connective define its meaning completely if and only if these rules are stable, which is harmony plus its converse. 13 Connectives that are not governed by stable rules require something other than purely logical rules in terms of which the grounds and consequences of assertions with them as main operator are specified and hence their meaning determined. 14 In the case of stable rules, the two processes of determining elimination rules from introduction rules and introduction rules from elimination rules lead to the same result (or at least to interderivable rules).…”

Section: Rules Of Typementioning

confidence: 99%

“…This discussion will undoubtedly have left some readers dissatisfied, but for more detailed discussion I must refer the reader to the literature quoted and further development must await another occasion. 13 See footnote 11. Other conditions may need to be in place, too, but these need not concern us here.…”

Section: Rules Of Typementioning

confidence: 99%

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Bilateral Inversion Principles

Kürbis

2022

Electron. Proc. Theor. Comput. Sci.

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This paper formulates a bilateral account of harmony that is an alternative to one proposed by Francez. It builds on an account of harmony for unilateral logic proposed by Kürbis and the observation that reading the rules for the connectives of bilateral logic bottom up gives the grounds and consequences of formulas with the opposite speech act. I formulate a process I call 'inversion' which allows the determination of assertive elimination rules from assertive introduction rules, and rejective elimination rules from rejective introduction rules, and conversely. It corresponds to Francez's notion of vertical harmony. I also formulate a process I call 'conversion', which allows the determination of rejective introduction rules from assertive elimination rules and conversely, and the determination of assertive introduction rules from rejective elimination rules and conversely. It corresponds to Francez's notion of horizontal harmony. The account has a number of features that distinguishes it from Francez's.

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Section: Introductionmentioning

confidence: 80%

Section: Rules Of Typementioning

confidence: 99%

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Bilateral Inversion Principles

Kürbis

2022

Electron. Proc. Theor. Comput. Sci.

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“…It is controversial that explosion and reductio ad absurdum are regarded as elimination rules of the logical connectives ⊥ and ¬, respectively. Rumfitt's bilateralism is also criticized in a paper [24]. That is, bilateralism is called a work in progress.…”

Section: Bilateral Natural Deductionsmentioning

confidence: 99%

A Symmetric Lambda-Calculus Corresponding to the Negation-Free Bilateral Natural Deduction

Abe,

Kimura

2021

Preprint

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Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive operators. That is, the duality of functions is not derived in the calculus but adopted as a principle of the calculus. In this paper, we propose a simple symmetric lambda-calculus corresponding to the negation-free natural deduction based bilateralism in proof-theoretic semantics. In our calculus, continuation types are represented as not negations of formulae but formulae with negative polarity. Function types are represented as the implication and but-not connectives in intuitionistic and paraconsistent logics, respectively. Our calculus is not only simple but also powerful as it includes a call-value calculus corresponding to the call-by-value dual calculus invented by Wadler. We show that mutual transformations between expressions and continuations are definable in our calculus to justify the duality of functions. We also show that every typable function has dual types. Thus, the duality of function is derived from bilateralism.

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“…Our approach in this paper is to remain as close to classical logic as possible while countenancing epistemic contradictions. Having said this, by modifying the negation rules or the coordination principles it is possible to provide bilateral logics with intuitionistic negation(Kürbis, 2016) or the paraconsistent negation of Nelson's logic N4(Drobyshevich, 2019).…”

mentioning

confidence: 99%

Epistemic Modals in Hypothetical Reasoning

Schlöder

Incurvati

Sbardolini

2022

Erkenn

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Data involving epistemic modals suggest that some classically valid argument forms, such as reductio, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a de re–de dicto collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic.

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Some Comments on Ian Rumfitt’s Bilateralism

Cited by 18 publications

References 8 publications

Bilateral Inversion Principles

Bilateral Inversion Principles

A Symmetric Lambda-Calculus Corresponding to the Negation-Free Bilateral Natural Deduction

Epistemic Modals in Hypothetical Reasoning

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