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(English and French summaries) [Strong stability and incompleteness of the class of stable models of pure /-calculus| C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), no. 10, 905-908. ... It is shown that the class of stable models is incomplete with respect to pure /-calculus; more precisely: there is no stable model the theory of which is the theory of Park’s strongly stable model. ...
Summary: “Lambda-calculus is the core of functional program- ming, and many different ways to evaluate lambda-terms have been considered. ... For the fixed-point condition (NS) of negation-stability, classical logic is negation-stable over itself, while intuitionistic logic is not. ...
We prove that the class of stable models is incomplete with respect to pure -calculus. More precisely, we show that no stable model has the same theory as the strongly stable version of Park's model. ... Finally, using an approximation theorem suitable for a large class of models (in particular stable and strongly stable non-sensible models like P fs and Ps), we prove that Th(Ps) and Th(P fs ) are included ... Acknowledgements Thanks are due to the anonymous referee, who provided detailed criticisms of previous versions of the paper. ...doi:10.1016/s0168-0072(99)00015-9 fatcat:7uzqav2wxfawnn3brctdiztn2q
, J.C. and MOGGI, E., Kripke-style models for typed lambda calculus MITCHELL, J., see LINCOLN, P. ... arithmetic MAREK, W., NERODE, A. and REMMEL, J., How complicated is the set of stable models of a recursive logic program? ...doi:10.1016/0168-0072(93)90081-n fatcat:izewemprtbcm3gozu2y4c4roia
We present a typed functional calculus that emphasizes the strong connection between the structure of whole pattern de nitions and their types. ... In the spirit of the Curry-Howard isomorphism, we design the calculus as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. ... Acknowledgments We are grateful, for helpful discussions, to Peter Buneman, Roberto Di Cosmo, Emmanuel Engel, Jean Gallier, Brian Howard, and Dan Suciu. ...doi:10.1006/inco.1996.0004 fatcat:zusdvxfve5dl3f7pp2i6wfap6e
The approach is implemented by means of a front-end to the mCRL2 tool set and illustrated for the switching of bacteriophage lambda and a bio-medical case study related to TGFβ driven fibrotic conditions ... Identification of bisimilar states yields a compact system representation truthfully expressing the information relevant for deciding logical properties. ... , 0, 0) form a stable cycle, nodes 34 and 35, refined model for the lambda phage via the formula Figure 13 : 13 partial LTS under maximal progress Figure 14 : 14 cII influence under maximal progress ...doi:10.1145/1839764.1839773 dblp:conf/cmsb/KrauseKV10 fatcat:2jog6paaxnefrhoes74h4sne4i
This categorical structure is also known as the computational lambda calculus c Moggi, 1989] . The application of c as a calculus of proofs for PLL has been investigated by Benton et al. ... Thus, the modality is used to account for the stability and timing constraints, which are no longer part of the speci cation but of the semantic model and of the correctness proofs. ...doi:10.1006/inco.1997.2627 fatcat:3qxkcqrgzndannymnngg6vss3a
and ordered, one after the other) and to the shared image of the width less continuous line, an abstracted trajectory, as practice of action in space (and time). ... They are "images", in the broad sense of mental constructions of a figurative nature: we will largely refer to the well ordering of integer numbers (they appear to our constructed imagination as spaced ... Our background in lambda-calculus and constructive proofs ( [Girard, 1990] ) has played an important role in the approach we have chosen. ...doi:10.5281/zenodo.3929708 fatcat:xe5zt5wm5ngxviv5grs2mitn7y
strong relative incompleteness, 769 conditions for -, 769 strong representation theorems, 1061 strong restriction, 685 of paramodulation for locking resolution, 685 strong satisfiability, 1742 ... , 3324.3580 for the polymorphic lambda calculus, 1552 result, 2321 strong NP-completeness, 249, 3306 NP-complete problems, 249 polymorphic typing, 2957 polynomial-time reducibilities, 1638 ...doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm
We survey or raise a lot of natural questions which arise when one tries to develop a model theory for untyped -calculus, in the sense of a general study of the relations between its models and its equational ... We focus on two methods: completion of partial webs (for building models) and reducibility (for studying them). ... Schonÿeld and A. Salibra for pertinent remarks, and M. Schonÿeld and D. Pelletier for kindly revising the English of substantial parts of the two successive versions. ...doi:10.1016/s0304-3975(00)00057-8 fatcat:7uqeoycgbnhivpgqyfm6ba6ate
Parsing the Turing Test
From the physico-mathematical view point, the imitation game between man and machine, proposed by Turing in his 1950 paper for the journal "Mind", is a game between a discrete and a continuous system. ... Turing's hinted distinction between imitation and modelling is developed, jointly to a discussion on the repeatability of computational processes in relation to physical systems. ... A question from Jean Petitot and his interest have encouraged me to clarify ...doi:10.1007/978-1-4020-6710-5_23 fatcat:tbybvft3tzfjzhwb3t3xilti4q
Lamarche, Stable domains are generalized topological spaces 111 (l-2) (1993) 103-123 152. M.G. Main, Comp!ete proof rules for strong fairness and strong extreme fairness R.D. Bomgin and S.E. ... Le Sate and 1. Litovsky, Stability for the zigzag submonoids 108 (2) (1993) 237-249 114. M. Madonia, S. Salemi and T. ...doi:10.1016/0304-3975(95)90002-0 fatcat:b7nmywx4tff6lhcd3jkoagotrm
of distance making the set of terms an incomplete metric space; the completion of this space is shown to yield an infinitary affine lambda-calculus, whose quotient under a suitable partial equivalence ... We seek a computational version of this phenomenon, with the idea that the role of the rationals should be played by the affine lambda-calculus, whose dynamics is finitary; the full lambda-calculus should ... Acknowledgments We are thankful to Michele Pagani and Rune Bak for interesting discussions on the subject of this paper. ...doi:10.1109/lics.2012.57 dblp:conf/lics/Mazza12 fatcat:ldqkg5sxyzb75lfgmanlhbwsl4
Constructtve proofs of the range property m lambda calculus 121 (I -2) (1993) 59-69 314. A. Berarducci and B. Intrigila, Some new results on easy lambda-terms 121 (l-2) (1993) 71-88 315. R.L. ... Stability for the ztgzag submonoids I 15. M. Dietzfelbinger and W. Maass, The complexity of matrtx transpositton on one-tape off-line Turing 117. R. Bar Yehuda, T. Etzton and S. Moran. ...doi:10.1016/0304-3975(95)80003-4 fatcat:5nnk76aalje5potfoeg7hksbce
Lecture Notes in Computer Science
The categorical framework enables to interpret the lambda-calculus, the logical skeleton of many programming languages, as well as extensions of the lambda-calculus (with references, exceptions, etc.) ... In a similar fashion, observations on a particular model lead Jean-Yves Girard to linear logic, a logic where hypothesis are seen as resources, or more recently, Thomas Ehrhard to differential lambda-calculus ... The prerequisites to the course are a good knowledge of differential calculus and probability theory from the viewpoint of measure theory. ...doi:10.1007/3-540-44842-x_84 fatcat:u3fiekkairaqrmmzgszuewociq
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