[1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science

15-18 July 1991

Filter Results

Displaying Results 1 - 25 of 41
  • Proceedings of Sixth Annual IEEE Symposium on Logic in Computer Science (Cat. No.91CH3025-4)

    Publication Year: 1991
    Request permission for reuse | PDF file iconPDF (126 KB)
    Freely Available from IEEE
  • A foundational delineation of computational feasibility

    Publication Year: 1991, Page(s):2 - 11
    Cited by:  Papers (14)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (701 KB)

    A principle directly pertinent to feasibility, which justifies the identification of P-time with feasible computing, is proposed. It is shown that the computable functions justified on the basis of positive quantifier-free comprehension are precisely the functions computable in deterministic polynomial time. This shows that the class P-time arises naturally from a foundational analysis of feasibil... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Toward a semantics for the QUEST language

    Publication Year: 1991, Page(s):12 - 21
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (668 KB)

    A model is given for the second-order lambda calculus extended with inheritance, bounded quantification, recursive types, constructors and kinds. This language, called mu -FunK, can be viewed as the core of the QUEST language defined by L. Cardelli (SRC Rep. 45, 1989). Types are interpreted as intervals of partial equivalence relations. Because of the properties of intervals and their ordering, al... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Term declaration logic and generalised composita

    Publication Year: 1991, Page(s):22 - 30
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (604 KB)

    A generalization of a version of order-sorted logic and an abstract axiomatic setting for the treatment of substitution are given. The two ideas are shown to be related, an equational specification of term declaration logic being a presentation of a finitary generalized composition. The automatic approach to substitution is compared with some other approaches. The relationship between algebraic th... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Logic programming in a fragment of intuitionistic linear logic

    Publication Year: 1991, Page(s):32 - 42
    Cited by:  Papers (18)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (774 KB)

    The intuitionistic notion of context is refined by using a fragment of J.-Y. Girard's (Theor. Comput. Sci., vol.50, p.1-102, 1987) linear logic that includes additive and multiplicative conjunction, linear implication, universal quantification, the of course exponential, and the constants for the empty context and for the erasing contexts. It is shown that the logic has a goal-directed interpretat... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Games semantics for linear logic

    Publication Year: 1991, Page(s):43 - 50
    Cited by:  Papers (29)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (523 KB)

    An attempt is made to relate various notions of duality used in mathematics with the denotational semantics of linear logic. The author proposes a naive semantics for linear logic that, in a certain sense, generalizes various notions such as finite-dimensional vector spaces, topological spaces, and J.-Y. Girard's (1987) coherence spaces. A game consists of a set of vectors (or strategies), a set o... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Linearizing intuitionistic implication

    Publication Year: 1991, Page(s):51 - 62
    Cited by:  Papers (8)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (670 KB)

    An embedding of the implicational propositional intuitionistic logic (IIL) into the nonmodal fragment of intuitionistic linear logic (IMALL) is given. The embedding preserves cut-free proofs in a proof system that is a variant of IIL. The embedding is efficient and provides an alternative proof of the PSPACE-hardness of IMALL. It exploits several proof-theoretic properties of intuitionistic implic... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Some results on the interpretation of lambda -calculus in operator algebras

    Publication Year: 1991, Page(s):63 - 72
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (709 KB)

    J.-Y. Girard (Proc. ASL Meeting, 1988) proposed an interpretation of second order lambda -calculus in a C algebra and showed that the interpretation of a term is a nilpotent operator. By extending to untyped lambda -calculus the functional analysis interpretation for typed lambda -terms, V. Danos (Proc. 3rd Italian Conf. on Theor. Comput. Sci., 1989) showed that all and only strongly normalizable ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Unification and anti-unification in the calculus of constructions

    Publication Year: 1991, Page(s):74 - 85
    Cited by:  Papers (25)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (772 KB)

    Algorithms for unification and anti-unification in the calculus of constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higher-order patterns, are presented. Most general unifiers and least common anti-instances are shown to exist and are unique up to a simple equivalence. The unification algorithm is used for logic program execution and typ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Partial objects in the calculus of constructions

    Publication Year: 1991, Page(s):86 - 95
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (611 KB)

    A typed framework for working with nonterminating computations is provided. The basic system is the calculus of constructions. It is extended using an original idea proposed by R. Constable and S.F. Smith (2nd Ann. IEEE Conf. on Logic in Comput. Sci., 1987) and implemented in Nuprl. From the computational point of view, an equivalent of the Kleene theorem for partial recursive functions over the i... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • An evaluation semantics for classical proofs

    Publication Year: 1991, Page(s):96 - 107
    Cited by:  Papers (36)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (922 KB)

    It is shown how to interpret classical proofs as programs in a way that agrees with the well-known treatment of constructive proofs as programs and moreover extends it to give a computational meaning to proofs claiming the existence of a value satisfying a recursive predicate. The method turns out to be equivalent to H. Friedman's (Lecture Notes in Mathematics, vol.699, p.21-28, 1978) proof by A-t... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A theory of testing for real-time

    Publication Year: 1991, Page(s):110 - 119
    Cited by:  Papers (16)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (663 KB)

    A framework for generating testing preorders that relate processes on the basis of their timing behavior as well as their degree of relative nondeterminism is developed. The basic concepts of transition systems and testing are reviewed, and timed testing, which takes account of the delay exhibited by a process as it attempts to pass a test, is introduced. The framework is then applied to two diffe... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Complexity bounds of Hoare-style proof systems

    Publication Year: 1991, Page(s):120 - 126
    Cited by:  Papers (1)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (576 KB)

    A refinement of the result that there is no sound and relatively complete proof system for a programming language if its partial correctness theory is undecidable even in finite interpretations is presented. By taking into account the computational complexity of this problem, information about structural properties of proof systems for a given programming language is obtained. The key in the proof... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Semantics of pointers, referencing and dereferencing with intensional logic

    Publication Year: 1991, Page(s):127 - 136
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (750 KB)

    Intensional logic is applied to the semantics of an Algol-like programming language. This approach associates with expressions their senses, or meanings relative to possible worlds, here interpreted as machine states. These meanings lie in the semantic domains of a higher order typed intensional logic. The advantage of the approach is that it preserves compositionality of the meaning function, eve... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Sequentiality and strong stability

    Publication Year: 1991, Page(s):138 - 145
    Cited by:  Papers (22)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (555 KB)

    It is shown that Kahn-Plotkin sequentiality can be expressed by a preservation property similar to stability and that this kind of generalized stability can be extended to higher order. The main result is the construction of a model where all morphisms are functions and, at ground types, these functions are sequential.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Parallel PCF has a unique extensional model

    Publication Year: 1991, Page(s):146 - 151
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (367 KB)

    It is shown that the continuous function model is the unique extensional (but not necessarily pointwise ordered) model of the variant of the applied typed lambda calculus PCF that includes the parallel or operation. It is also shown that parallel PCF does not have extensional models that are not inequationally fully abstract or not even equationally fully abstract or extensional models that are no... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The fixed point property in synthetic domain theory

    Publication Year: 1991, Page(s):152 - 160
    Cited by:  Papers (9)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (554 KB)

    An elementary axiomatization of synthetic domain theory is presented, and it is shown that it is sufficient to deduce the fixed point property and solve domain equations. The aim is to show that an important theorem can be derived from an abstract axiomatization, rather than from a particular model. Also, by providing a common framework in which both PER and classical models can be expressed, this... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On computational open-endedness in Martin-Lof's type theory

    Publication Year: 1991, Page(s):162 - 172
    Cited by:  Papers (9)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (834 KB)

    Computational open-endedness in a type theory is defined as the property that theorems remain true under extensions to the underlying programming language. Some properties related to open-endedness that are relevant to machine implementations of type theory are established. A class of computation systems, specified by a simple but fairly general kind of structural operational semantics, with respe... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Predictive type universes and primitive recursion

    Publication Year: 1991, Page(s):173 - 184
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (698 KB)

    A category-theoretic explanation of predicative type universes and primitive recursion on them is given. Categories with display maps (cdm) (with canonical pullbacks) are used to model families. A slight generalization of an algebra, called an I-algebra, is given. Primitive recursion is defined, and the general definition of primitive recursion on a cdm which can justify the elimination rules for ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Freyd's hierarchy of combinator monoids

    Publication Year: 1991, Page(s):186 - 190
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (251 KB)

    The Freyd hierarchy of monoids is introduced. The Freyd hierarchy is a fragment of type-free combinatory algebra lambda -calculus that has some remarkable properties, some of which are presented. One result characterizes the combinators in the hierarchy in terms of some simple ideas from the theory of rewrite rules. The computational/expressive power of the fragment is studied. This includes not o... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Equational programming in lambda -calculus

    Publication Year: 1991, Page(s):191 - 202
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (786 KB)

    A system of equations in lambda -calculus is a pair ( Gamma , X) where Gamma is a set of formulas of Lambda (the equations) and X is a finite set of variables of Lambda (the unknowns). A system S=( Gamma , X) is said to be solvable in the theory T (T-solvable) if there exists a simultaneous substitution with closed lambda -terms for the unknowns that makes the formulas of Gamma theorems in the the... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • An inverse of the evaluation functional for typed lambda -calculus

    Publication Year: 1991, Page(s):203 - 211
    Cited by:  Papers (34)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (664 KB)

    A functional p to e (procedure to expression) that inverts the evaluation functional for typed lambda -terms in any model of typed lambda -calculus containing some basic arithmetic is defined. Combined with the evaluation functional, p to e yields an efficient normalization algorithm. The method is extended to lambda -calculi with constants and is used to normalize (the lambda -representations of)... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A completeness theorem for Kleene algebras and the algebra of regular events

    Publication Year: 1991, Page(s):214 - 225
    Cited by:  Papers (29)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (677 KB)

    A finitary axiomatization of the algebra of regular events involving only equations and equational implications that is sound for all interpretations over Kleene algebras is given. Axioms for Kleene algebra are presented, and some basic consequences are derived. Matrices over a Kleene algebra are considered. The notion of an automaton over an arbitrary Kleen algebra is defined and used to derive t... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On first order database query languages

    Publication Year: 1991, Page(s):226 - 231
    Cited by:  Papers (3)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (499 KB)

    Using methods from model theory, the authors construct algorithms that, given any first-order predicate calculus query over a finite database, determine if they have a finite number of solutions or not, and if they do, list them all. This is done for languages that include function names (but no symbols for infinite relations) and for languages that include a name for the order of natural number o... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Specifying and proving serializability in temporal logic

    Publication Year: 1991, Page(s):232 - 244
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (1112 KB)

    Serializability of database transactions is first defined within the framework of linear temporal logic. For commutativity-based serializability, an alternative specification is given in a temporal logic whose semantic interpretation is especially tailored for reasoning about equivalence sequences of histories. The alternative specification method is given in ISTL* and is limited to the specificat... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.