A Gentzen-style sequent calculus of constructions with expansion rules

Seldin, Jonathan P.

doi:10.1016/s0304-3975(98)00195-9

Cited by 7 publications

(7 citation statements)

References 2 publications

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“…Huet (1986, 1988), and the related metatheoretical analysis, e.g. Seldin (1997Seldin ( , 2000. Similarly, a sequent calculus can be formulated that reflects the operations of becoming informed as operations on antecedents of sequents.…”

Section: Going Modalmentioning

confidence: 99%

An epistemic logic for becoming informed

Primiero¹

2008

Synthese

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Various conceptual approaches to the notion of information can currently be traced in the literature in logic and formal epistemology. A main issue of disagreement is the attribution of truthfulness to informational data, the so called Veridicality Thesis (Floridi 2005). The notion of Epistemic Constructive Information (Primiero 2007) is one of those rejecting VT. The present paper develops a formal framework for ECI. It extends on the basic approach of Artemov's logic of proofs (Artemov 1994), representing an epistemic logic based on dependent justifications, where the definition of information relies on a strict distinction from factual truth. The definition obtained by comparison with a Normal Modal Logic translates a constructive logic for "becoming informed": its distinction from the logic of "being informed"-which internalizes truthfulness-is essential to a general evaluation of information with respect to truth. The formal disentanglement of these two logics, and the description of the modal version of the former as a weaker embedding into the latter, allows for a proper understanding of the Veridicality Thesis with respect to epistemic states defined in terms of information.

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Section: Going Modalmentioning

confidence: 99%

An epistemic logic for becoming informed

Primiero¹

2008

Synthese

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“…We adopted the guideline that only proof-expression could suffer a change in the proof-theoretical format, but other, more "uniform", possibilities exist, where also the domain assignment relation is changed to the sequent calculus format. An improvement, in view of proof-search, is to restrict the conversion rule of the typing system to an expansion rule [36]. Finally, in λHJ mse , λωJ mse , and λ2J mse we re-encounter explicit substitutions in higher-order type theories [4,28], but with a simpler treatment (no explicit execution) and in a simpler setting (no dependent types).…”

Section: Cgps Translationsmentioning

confidence: 99%

Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

Santo

Matthes

Pinto

2007

Lecture Notes in Computer Science

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Abstract. The intuitionistic fragment of the call-by-name version of Curien and Herbelin's λµμ-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed λ-calculus. Our embedding is a continuation-and-garbagepassing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's λµ-calculus. The embedding strictly simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed λ-calculus leading to our intuitionistic system, and already for the simplest extension we consider (λ-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding. The results obtained extend to second and higher-order calculi.

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“…If both the abstraction and conversion rules are modified, "AC" will be added to the name. The original TOC0 of Seldin [6,[12][13][14][15][16] is, in this notation, TOC0AC. 4 As we shall see below, TOC0-like systems and TOC2-like systems with the same letters on the end are equivalent.…”

Section: The Different Variantsmentioning

confidence: 99%

“…TOC2P is a restriction of the system called TOC2 in [13,37]. Seldin [6,[12][13][14][15][16] writes (∀x : A)B and others write (Πx : A)B for (Πx : A.B). In PTSs, it is standard to use * for Prop and P for Type.…”

Section: Remarkmentioning

confidence: 99%

“…Seldin was thus led to systems significantly more general than the original formulation of Coquand and Huet. Originally, Seldin did not think these differences were terribly important, and he continued to use these versions in [6,[12][13][14][15][16]. Recently, however, Seldin has been asked on several occasions about the exact relationship between his versions and the other ones.…”

Section: Introductionmentioning

confidence: 99%

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Variants of the basic calculus of constructions

Bunder

Seldin

2004

Journal of Applied Logic

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In this paper, a number of different versions of the basic calculus of constructions that have appeared in the literature are compared and the exact relationships between them are determined. The biggest differences between versions are those between the original version of Coquand and the version in early papers on the subject by Seldin. None of these results is very deep, but it seems useful to collect them in one place.

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A Gentzen-style sequent calculus of constructions with expansion rules

Cited by 7 publications

References 2 publications

An epistemic logic for becoming informed

An epistemic logic for becoming informed

Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

Variants of the basic calculus of constructions

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