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Jose Espirito Santo - One of the best experts on this subject based on the ideXlab platform.
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towards a canonical classical natural deduction system
Annals of Pure and Applied Logic, 2013Co-Authors: Jose Espirito SantoAbstract:Abstract This paper studies a new classical natural deduction system, presented as a typed calculus named λ μ let . It is designed to be isomorphic to Curien and Herbelinʼs λ ¯ μ μ ˜ -calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigotʼs λμ-calculus with the idea of “coercion calculus” due to Cervesato and Pfenning, accommodating let-expressions in a surprising way: they expand Parigotʼs syntactic class of named terms. This calculus and the mentioned isomorphism Θ offer three missing components of the proof theory of classical logic: a canonical natural deduction system; a robust process of “read-back” of calculi in the sequent calculus format into natural deduction syntax; a formalization of the usual semantics of the λ ¯ μ μ ˜ -calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. λ μ let is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus; and Θ provides the “read-back” map and the formalized semantics, based on the precise notions of context and “hole-expression” provided by λ μ let . We use “read-back” to achieve a precise connection with Parigotʼs λμ, and to derive λ-calculi for call-by-value combining control and let-expressions in a logically founded way. Finally, the semantics Θ, when fully developed, can be inverted at each syntactic category. This development gives us license to see sequent calculus as the semantics of natural deduction; and uncovers a new syntactic concept in λ ¯ μ μ ˜ (“co-context”), with which one can give a new definition of η-reduction.
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towards a canonical classical natural deduction system
Computer Science Logic, 2010Co-Authors: Jose Espirito SantoAbstract:This paper studies a new classical natural deduction system, presented as a typed calculus named λµlet. It is designed to be isomorphic to Curien-Herbelin's λµµ-calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's λµ-calculus with the idea of "coercion calculus" due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. λµlet is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of λµµ-calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by λµlet. The third problem is the lack of a robust process of "read-back" into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of λ-calculi for call-byvalue. An isomorphic counterpart to the Q-subsystem of λµµ-calculus is derived, obtaining a new λ-calculus for call-by-value, combining control and let-expressions.
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an isomorphism between a fragment of sequent calculus and an extension of natural deduction
Lecture Notes in Computer Science, 2002Co-Authors: Jose Espirito SantoAbstract:Variants of Herbelin's A-calculus, here collectively named Herbelin calculi, have proved useful both in foundational studies and as internal languages for the efficient representation of A-terms. An obvious requirement of both these two kinds of applications is a clear understanding of the relationship between cut-elimination in Herbelin calculi and normalisation in the A-calculus. However, this understanding is not complete so far. Our previous work showed that A is isomorphic to a Herbelin calculus, here named AP, only admitting cuts that are both left- and right-permuted. In this paper we consider a generalisation APh admitting any kind of right-permuted cut. We show that there is a natural deduction system λNh which conservatively extends A and is isomorphic to APh. The idea is to build in the natural deduction system a distinction between applicative term and application, together with a distinction between head and tail application. This is suggested by examining how natural deduction proofs are mapped to sequent calculus derivations according to a translation due to Prawitz. In addition to β, λNh includes a reduction rule that mirrors left permutation of cuts, but without performing any append of lists/spines.
Carsten Schurmann - One of the best experts on this subject based on the ideXlab platform.
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focused natural deduction
International Conference on Logic Programming, 2010Co-Authors: Taus Brocknannestad, Carsten SchurmannAbstract:Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction and the backward linear focusing calculus.
Silvia Likavec - One of the best experts on this subject based on the ideXlab platform.
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strong normalization of the dual classical sequent calculus
International Conference on Logic Programming, 2005Co-Authors: Daniel J. Dougherty, Silvia Ghilezan, Pierre Lescanne, Silvia LikavecAbstract:We investigate some syntactic properties of Wadler’s dual calculus, a term calculus which corresponds to classical sequent logic in the same way that Parigot’s λμ calculus corresponds to classical natural deduction. Our main result is strong normalization theorem for reduction in the dual calculus; we also prove some confluence results for the typed and untyped versions of the system.
Tanya Fiedler - One of the best experts on this subject based on the ideXlab platform.
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Seduction as control gamification at foursquare
Management Accounting Research, 2021Co-Authors: Christopher S Chapman, Wai Fong Chua, Tanya FiedlerAbstract:Abstract Post-disciplinary accounting research has drawn attention to the potential for technologies such as big data analytics and social media to enact new forms of surveillance and control, thereby transforming work, identity and producing anxiety. This paper explores these concerns in the context of the growing popularity of the use of game design elements in non-game settings (gamification). By drawing on Baudrillard’s (1990) theorisation of Seduction, this paper argues that gamification, as Seduction, is a mode of post-disciplinary control. We develop our analysis through an illustrative case of Foursquare, a gamified location-based platform organisation. We show how Foursquare exercises control; seducing its users by creating a communal, gamified milieu of symbolic exchange which is distinct from but connected to the commodity exchanges that underpin its business model. Gamification seduces users to play, travel and ‘arrange’ their bodies in particular temporal and spatial settings in exchange for the virtual rewards, feelings of pleasure, and sense of community gamification affects. In playing, users have fun, become part of an online community, give of their bodily work and associated biodata, and so they drive commodity exchange and the production of economic value for Foursquare and its partners.
Taus Brocknannestad - One of the best experts on this subject based on the ideXlab platform.
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focused natural deduction
International Conference on Logic Programming, 2010Co-Authors: Taus Brocknannestad, Carsten SchurmannAbstract:Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction and the backward linear focusing calculus.