Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science

4-7 July 1994

Filter Results

Displaying Results 1 - 25 of 54
  • Higher-order narrowing

    Publication Year: 1994, Page(s):507 - 516
    Cited by:  Papers (7)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (853 KB)

    Introduces several approaches for solving higher-order equational problems by higher-order narrowing, and gives some completeness results. The results apply to higher-order functional-logic programming languages and to higher-order unification modulo a higher-order equational theory. We lift the general notion of first-order narrowing to so-called higher-order patterns and argue that the full high... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Rigid E/spl I.oarr/-unifiability is DEXPTIME-complete

    Publication Year: 1994, Page(s):498 - 506
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (715 KB)

    Proves that rigid E/spl I.oarr/-unifiability, a decision problem invented by Gallier et al. (1987) to extend first-order tableaux-like proof procedures to first-order logic with equality, is DEXPTIME-complete; and that, when restricted to monadic terms, it is PSPACE-complete.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Language completeness of the Lambek calculus

    Publication Year: 1994, Page(s):487 - 496
    Cited by:  Papers (4)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (803 KB)

    Proves that the Lambek calculus (J. Lambek, American Math. Monthly, vol. 65, no. 3, pp. 154-170, 1958), which is essentially a subsystem of noncommutative linear logic, is complete with respect to L-models, i.e. free semigroup models.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A modal logic for subjective default reasoning

    Publication Year: 1994, Page(s):477 - 486
    Cited by:  Papers (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (873 KB)

    Introduces a logic endowed with a two-place modal connective that has the intended meaning of "if /spl alpha/, then normally /spl beta/". On top of providing a well defined tool for analyzing common default reasoning, such a logic allows nesting of the default operator. We present a semantic framework in which many of the known default proof systems can be naturally characterized, and prove soundn... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Logical bilattices and inconsistent data

    Publication Year: 1994, Page(s):468 - 476
    Cited by:  Papers (18)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (651 KB)

    The notion of a bilattice was first proposed by Ginsberg (1988) as a general framework for many applications. This notion was further investigated and applied for various goals by Fitting (1989, 1990, 1991, 1993). In this paper, we develop proof systems which correspond to bilattices in an essential way. We then show how to use those bilattices for efficient inferences from possibly inconsistent d... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Compositional verification of real-time systems

    Publication Year: 1994, Page(s):458 - 465
    Cited by:  Papers (19)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (463 KB)

    Presents a compositional proof system for the verification of real-time systems. Real-time systems are modeled as timed transition modules, which explicitly model interaction with the environment and may be combined using composition operators. Composition rules are devised such that the correctness of a system may be determined from the correctness of its components. These proof rules are demonst... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Axioms for knowledge and time in distributed systems with perfect recall

    Publication Year: 1994, Page(s):448 - 457
    Cited by:  Papers (9)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (918 KB)

    A distributed system, possibly asynchronous, is said to have perfect recall if at all times each processor's state includes a record of all its previous states. The completeness of a propositional modal logic of knowledge and time with respect to such systems is established. The logic includes modal operators for knowledge, and the linear time operators "next" and "until".<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A trace based extension of linear time temporal logic

    Publication Year: 1994, Page(s):438 - 447
    Cited by:  Papers (31)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (961 KB)

    The propositional temporal logic of linear time (PTL) is interpreted over linear orders of order type (/spl omega/,/spl les/). In applications, these linear orders consist of interleaved descriptions of the infinite runs of a concurrent program. Recent research on partial order based verification methods suggests that it might be fruitful to represent such runs as partial orders called infinite tr... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Paths in the lambda-calculus. Three years of communications without understanding

    Publication Year: 1994, Page(s):426 - 436
    Cited by:  Papers (8)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (887 KB)

    Since the rebirth of /spl lambda/-calculus in the late 1960s, three major theoretical investigations of /spl beta/-reduction have been undertaken: (1) Levy's (1978) analysis of families of redexes (and the associated concept of labeled reductions); (2) Lamping's (1990) graph-reduction algorithm; and (3) Girard's (1988) geometry of interaction. All three studies happened to make crucial (if not alw... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Modularity of strong normalization and confluence in the algebraic-/spl lambda/-cube

    Publication Year: 1994, Page(s):406 - 415
    Cited by:  Papers (8)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    Presents the algebraic-/spl lambda/-cube, an extension of Barendregt's (1991) /spl lambda/-cube with first- and higher-order algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraic-/spl lambda/-cube, provided that the first-order rewrite rules are non-duplicating and the higher-order rules satisfy the general schema of Jouannaud and Okada (1991)... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Normalised rewriting and normalised completion

    Publication Year: 1994, Page(s):394 - 403
    Cited by:  Papers (11)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (806 KB)

    Introduces normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, or the theory of commutative rings. We give a new completion algorithm for normalised rewriting. It contains as an instance the usual AC completion algorithm (AC bein... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Rewrite techniques for transitive relations

    Publication Year: 1994, Page(s):384 - 393
    Cited by:  Papers (16)  |  Patents (1)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (922 KB)

    We propose inference systems for dealing with transitive relations in the context of resolution-type theorem proving. These inference mechanisms are based on standard techniques from term rewriting and represent a refinement of chaining methods. We establish their refutational completeness and also prove their compatibility with the usual simplification techniques used in rewrite-based theorem pro... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Categories, allegories and circuit design

    Publication Year: 1994, Page(s):372 - 381
    Cited by:  Papers (6)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (825 KB)

    Relational languages such as RUBY are used to derive hardware circuits from abstract specifications of their behaviour. Much reasoning is done informally in RUBY using pictorial representations of relational terms. We formalise this use of pictures in circuit design. We show that pictures naturally form a unitary pretabular allegory. Homomorphisms of pictures correspond to adding new wires or circ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Reflexive graphs and parametric polymorphism

    Publication Year: 1994, Page(s):364 - 371
    Cited by:  Papers (7)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (686 KB)

    The pioneering work on relational parametricity for the second order lambda calculus was done by Reynolds (1983) under the assumption of the existence of set-based models, and subsequently reformulated by him, in conjunction with his student Ma, using the technology of PL-categories. The aim of this paper is to use the different technology of internal category theory to re-examine Ma and Reynolds'... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A general semantics for Evaluation Logic

    Publication Year: 1994, Page(s):353 - 362
    Cited by:  Papers (4)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (724 KB)

    The semantics of Evaluation Logic proposed by Moggi (1994) relies on additional properties of monads. This paper proposes an alternative semantics, which drops all additional requirement on monads at the expense of stronger assumptions on the underlying category. These assumptions are satisfied by any topos, but not by the category of cpos. However, in the setting of Synthetic Domain Theory (J. Hy... View full abstract»

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

    Publication Year: 1994, Page(s):342 - 352
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (931 KB)

    Most programming languages have certain phrases (like expressions) which only read information from the state and certain others (like commands) which write information to the state. These are called passive and active phrases respectively. Semantic models which make these distinctions have been hard to find. For instance, most semantic models have expression denotations that (temporarily) change ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A semantics of object types

    Publication Year: 1994, Page(s):332 - 341
    Cited by:  Papers (13)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (825 KB)

    We give a semantics for a typed object calculus, an extension of System F with object subsumption and method override. We interpret the calculus in a per model, proving the soundness of both typing and equational rules. This semantics suggests a syntactic translation from our calculus into a simpler calculus with neither subtyping nor objects.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the Church-Rosser property for expressive type systems and its consequences for their metatheoretic study

    Publication Year: 1994, Page(s):320 - 329
    Cited by:  Papers (7)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (940 KB)

    We consider two alternative definitions for the conversion rule in pure type systems. We study the consequences of this choice for the metatheory and point out the related implementation issues. We relate two open problems by showing that if a PTS allows the construction of a fixed point combinator, then Church-Rosser for /spl betaspl eta/-reduction fails. We present a new formalization of Russell... View full abstract»

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

    Publication Year: 1994, Page(s):310 - 319
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (929 KB)

    We study the interaction of subtyping and parametricity. We describe a logic for a programming language with parametric polymorphism and subtyping. The logic supports the formal definition and use of relational parametricity. We give two models for it, and compare it with other formal systems for the same language. In particular we examine the "Penn interpretation" of subtyping as implicit coercio... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The emptiness problem for intersection types

    Publication Year: 1994, Page(s):300 - 309
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (879 KB)

    We prove that it is undecidable whether a given intersection type is non-empty, i.e., whether there exists a closed term of this type.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Linear logic, totality and full completeness

    Publication Year: 1994, Page(s):292 - 298
    Cited by:  Papers (10)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (504 KB)

    I give a 'totality space' model for linear logic [4] derived by taking an abstract view of computations on a datatype. The model has similarities with both the coherence space model and game-theoretic models, but is based upon a notion of total object. Using this model, I prove a full completeness result. In other words, I show that the mapping of proofs to their interpretations (here collections ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Proof search in first-order linear logic and other cut-free sequent calculi

    Publication Year: 1994, Page(s):282 - 291
    Cited by:  Papers (10)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (804 KB)

    We present a general framework for proof search in first-order cut-free sequent calculi and apply it to the specific case of linear logic. In this framework, Herbrand functions are used to encode universal quantification, and unification is used to instantiate existential quantifiers so that the eigenvariable conditions are respected. We present an optimization of this procedure that exploits the ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A multiple-conclusion meta-logic

    Publication Year: 1994, Page(s):272 - 281
    Cited by:  Papers (19)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (909 KB)

    The theory of cut-free sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, /spl lambda/Prolog and its linear logic refinement, Lolli (J. Hodas and D. Miller, 1994), provide for various forms of abstraction (modules, abstract data types, higher-order programming) but lack primitives for concurrency. The logic programming la... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Semantics of meta-logic in an algebra of programs

    Publication Year: 1994, Page(s):262 - 270
    Cited by:  Papers (3)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (783 KB)

    Meta-programming is a powerful technique for extending and modifying the semantics of an existing object language. Along with the expressiveness, however, meta-programming puts forth some subtle semantic problems, among which the most critical is bound to the representation of object programs at the meta-level. We propose a semantic justification for a simple representation technique in the field ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The declarative semantics of the Prolog selection rule

    Publication Year: 1994, Page(s):252 - 261
    Cited by:  Papers (2)
    Request permission for reuse | Click to expandAbstract | PDF file iconPDF (860 KB)

    We axiomatize the Prolog selection rule which always selects the leftmost literal in a goal. We introduce a new completion of a logic program which we call the l-completion of the program. The l-completion is formulated as a first-order theory in a language extended by new predicate symbols which express success, failure and left-termination of queries. The main results of the paper are the follow... View full abstract»

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