Jawahar Lal Chirimar. Proof Theoretic Approach to Speci cation Languages. PhD thesis, University of Pennsylvania, May 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... For example, Miller outlines a translation from the calculus into linear logic: processes become LL propositions and calculus reduction becomes LL entailment [Mil92] These ideas are generalized and reformulated as a logical framework in Miller s proposal for the speci cation logic Forum [Mil96, Chi95]. Forum o ers a paradigm for viewing logic programming as concurrent computation, and so it is likely that the logic programming interpretation for CLF will draw heavily from it. However, in Forum proofs cannot be manipulated as rst class objects not even cut elimination is treated, let al..one an ....

Jawahar Lal Chirimar. Proof Theoretic Approach to Speci cation Languages. PhD thesis, University of Pennsylvania, May 1995.

....is captured by cut elimination (normalization) steps over linear logic derivations. A second direction, which may be identi ed with the slogan proofs as traces (and formulas as processes) models dynamic process behaviors as proof search, generally in the style of (linear) logic programming [MOM91,And92,Mil92,KY93,Chi95,Cer95]. CLF follows this second path, stressing a one to one correspondence between CLF proof terms and process executions (traces) CPWW02] CLF di ers from most of these proposals in two respects: rst, it is a fully edged logical framework, which means that it expresses not only the constructs of ....

Jawahar Lal Chirimar. Proof Theoretic Approach to Speci cation Languages. PhD thesis, University of Pennsylvania, May 1995.

.... p; q A ) q B (1) 1 The notion of an abstract logic programming language developed by Miller et al. ended up having a broader scope than we are considering here: uniform proof calculi may exist for carefully chosen presentations of linear and certain classical logics as well, see e.g. FORUM [5, 16]. 3 is replaced by: P j j= D G i P; D j j= G (2) where P and D must be program formulae and G a goal. Since the set of possible worlds is xed in advance, and consists of formulae, this semantics as far as programs are concerned contains only term models. This paper addresses this problem ....

Jawahar Chirimar. Proof Theoretic Approach to Specication Languages. PhD thesis, University of Pennsylvania, 1995.

....of linear logic, an interpretation in which sequents represent instant con gurations of a computation and where the logical rules describe its evolution. The result of a computation is the computed answer substitution associated to the proof. These aspects have been extensively studied in Forum [7,10,26], a powerful speci cation language complete with respect to higher order linear logic. Many aspects of Forum, however, rely on full linear logic and do not have an immediate operational reading according to traditional logic programming languages. For instance, Forum allows negative occurrences ....

.... : where and are sets of unbounded use formulas ( contains formulas and contains formulas) Forum (cut free) proofs are uniform in the following sense: the right hand side of sequents must be reduced to a multi set of atomic formulas before applying left introduction rules. In [7,26], several application of Forum to the speci cation of resource sensible logics and programming paradigms have been described. Implementations of a rst order formulation of Forum based on the I O model of [18] have been recently proposed by Hodas and Polakow in [19] and by L opez and Pimentel in ....

J. Chirimar. Proof Theoretic Approach to Specication Languages. PhD thesis, Department of Computer and Information Science, University of Pennsylvania, 1995.

....areas of Computer Science, and it has concrete prospects of in uencing the eld of security protocol analysis in a similar way. As a speci cation language, linear logic has been used to provide elegant and e ective representations of many systems that share characteristics with cryptoprotocols [8, 9, 17, 18]. The natural embedding of concurrent systems in linear logic [15, 20] in particular in its graphbased presentations [16] is also likely to be relevant, given the interpretation of security protocols as concurrent systems [1, 40] Work on meta reasoning in linear logic [32] promises to address ....

Chirimar, J. L. Proof Theoretic Approach to Specication Languages. PhD thesis, Department of Computer and Information Science, University of Pennsylvania, 1995.

....areas of Computer Science, and it has concrete prospects of in uencing the eld of security protocol analysis in a similar way. As a speci cation language, linear logic has been used to provide elegant and e ective repre1 sentations of many systems that share characteristics with crypto protocols [6, 7, 15, 16]. The natural embedding of concurrent systems in linear logic [13, 18] in particular in its graph based presentations [14] is also likely to be relevant, given the interpretation of security protocols as concurrent systems [1, 31] Work on meta reasoning in linear logic [25] promises to address ....

J. L. Chirimar. Proof Theoretic Approach to Specication Languages. PhD thesis, Department of Computer and Information Science, University of Pennsylvania, 1995.

....is provable, with N corresponding to the notion 30 of answer substitution. Sequent calculi can be used only to express deductions between formulae of the logic but if we take into account a given interpretation (for instance formulae as processes [89] they can be used to represent speci cations [33], properties [106] or computations (for instance, reduction of processes, i.e. P P 0 interpreted as P P 0 ) Consider Prolog and its linear logic re nement, Lolli. They provide for various forms of abstraction (abstract data types, modules, higher order programming) but lack primitives ....

J. Chirimar. Proof Theoretic Approach to Specication Languages. PhD thesis, Department of Computer and Information Science, University of Pennsylvania, 1995.

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Jawahar Lal Chirimar. Proof Theoretic Approach to Speci cation Languages. PhD thesis, University of Pennsylvania, May 1995.

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Jawahar Chirimar, Proof theoretic approach to speci cation languages, Ph.D. thesis, University of Pennsylvania, February 1995.

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Jawahar Chirimar. Proof Theoretic Approach to Speci cation Languages. PhD thesis, University of Pennsylvania, February 1995.

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