Computational Interpretation Research Articles

New Foundations for the Geometry of Interaction

A new formal embodiment of J.-Y. Girard's (1989) geometry of interaction program is given. The geometry of interaction interpretation considered is defined, and the computational interpretation is sketched in terms of dataflow nets. Some examples that illustrate the key ideas underlying the interpretation are given. The results, which include the semantic analogue of cut-elimination, stated in terms of a finite convergence property, are outlined. >

Linear logic as a logic of computations

The question at issue is to develop a computational interpretation of Linear Logic [8] and to establish exactly its expressive power. We follow the bottom-up approach. This involves starting with the simplest of the systems we are interested in, and then expanding them step-by-step. We begin with the !-Horn fragment of Linear Logic, which uses only positive literals, the linear implication ⊸, the tensor product ⊗, and the modal storage operator !. We give a complete computational interpretation for the !-Horn fragment of Linear Logic and for some natural generalizations of it formed by introducing additive connectives. Here we use the well-known ‘ or’-like connective ⊕, and, for the sake of the computational duality, we introduce a new ‘ and’-like connective @ For !-Horn sequents, we prove that their derivability problem is directly equivalent to the reachability problem for Petri nets, which is known to be decidable [19]. For the (!, ⊕)-Horn fragment of Linear Logic, which uses only positive literals, the linear implication ⊸, the tensor product ⊗, the modal storage operator!, and the additive ‘disjunction’ ⊕, we prove that standard Minsky machines [21] can be directly encoded in this (!, ⊕)-Horn fragment. Standard Minsky machines can be directly encoded in the corresponding ‘dual’ (!, @)-Horn fragment of Linear Logic, as well. As a corollary, both these fragments of Linear Logic are proved to be undecidable.

Computational interpretations of linear logic

We study Girard's linear logic from the point of view of giving a concrete computational interpretation of the logic, based on the Curry—Howard isomorphism. In the case of Intuitionistic linear logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cut-elimination. In the classical case, it leads to a concurrent process paradigm with an operational semantics in the style of Berry and Boudol's chemical abstract machine. This opens up a promising new approach to the parallel implementation of functional programming languages; and offers the prospect of typed concurrent programming in which correctness is guaranteed by the typing.

Molecular mechanics of bridged ferrocene derivatives: Conformational energy surfaces of [3]‐, [4]‐ and [45] ferrocenophanes

AbstractA molecular mechanical model is presented which allows computational interpretation of stereodynamics in ferrocenophanes by using a simple form of bending potential for angles involving the central iron atom and extended to carbon atoms of different cyclopentadienyl rings. Potential energy surfaces of [3] ‐, [4] ‐ and [45] ferrocenophanes were studied in detail. For [3] ferrocenophane, the calculated energy barrier of the bridge reversal process agrees well with the experimental value. The previous interpretation of a rigid bridge in [4] ferrocenophane is questioned on the basis of the calculated low barriers. The predominance of experimentally indistinguishable enantiomeric pairs may be responsible for the misinterpretation. [45] Ferrocenophane is estimated to interconvert into D5‐symmetric global energy minima over barriers of 13–15 kcal mol−1 through one‐by‐one flipping of five tetramethylene bridges.

An intuitionistic theory of types with assumptions of high-arity variables

Bossi, A. and S. Valentini, An intuitionistic theory of types with assumptions of high-arity variables, Annals of Pure and Applied Logic 57 (1992) 93–149. After an introductory discussion on Martin-Löf's Intuitionistic Theory of Types (ITT), the paper introduces the notion of assumption of high-arity variable. Then the original theory is extended (HITT) in a very uniform way by means of the new assumptions. Some improvements allowed by high-arity variables are shown. The main result of the paper is a normal form theorem for HITT. The detailed proof follows a computability method ‘a la Tait’. The main consequences of the normal form theorem are: the consistency of HITT, which also implies the consistency of ITT, and the computability of any judgement derived within HITT. Besides that, a canonical form theorem is shown: to any derivable judgement we can associate a canonical one whose derivation ends with an introductory rule. The standard disjunction and existential properties follow. Moreover, by using the computational interpretation of types it immediately follows that the execution of any proved correct program terminates.

On systems of definitions, induction and recursion

Primitive recursion can be seen as the computational interpretation of induction through the Curry-Howard interpretation of propositions-as-types. In the present paper we discuss what happens if we apply this idea to possible non monotone inductive definitions. We start with a logical interpretation of a class of inductive definitions, thepartial inductive definitions. Then we internalise induction over such definitions as a rule of inference and consider a Curry-Howard interpretation of these definitions as type systems. As a basic example we discuss what meaning this interpretation gives to primitive recursion on a definition likeN=N→N.

FROM PETRI NETS TO LINEAR LOGIC THROUGH CATEGORIES: A SURVEY

Linear logic has been introduced by Girard as a logic of actions that seems well suited for concurrent computation. This paper surveys recent work on the applications of linear logic to concurrency, with special emphasis on Petri nets and on the use of categorical models. In particular, we present a synthesis of our previous work on the systematic correspondence between Petri nets, linear logic theories, and linear categories, and explain its relationships to work by many other authors. Throughout, we discuss the computational interpretation of the linear logic connectives and illustrate the ideas with examples. Categories play an important role in this survey. On the one hand, from a computational perspective, they are interpreted as concurrent systems whose objects are states, and whose morphisms are transitions; on the other hand, when a model-theoretic perspective is adopted, they provide a very flexible conceptual framework within which the relationships among quite different models already proposed for linear logic can be better understood; this framework also suggests the study of new models and an axiomatic treatment of classes of models. Our categorical semantics for linear logic is based on dualizing objects and permits a very simple presentation of ideas requiring a more complicated treatment in the language of *-autonomous categories.

Induction log modeling using vertical eigenstates

A mode-matching method for models involving both horizontal and vertical interfaces is presented. In this method, the solution is represented in terms of modes inside and outside the borehole, and the modes are matched on the borehole wall to yield the solution. The method uses vertical modes (i.e. modes defined with respect to the vertical coordinate z). The receiver signal consists of a direct signal traveling within the borehole and a reflection signal bearing information about the rock formation outside the borehole. Compared to previous methods using modes defined with respect to the horizontal coordinate, the present method has advantages in terms of computational efficiency and data interpretation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phonological events

One of the major innovations within post-SPE generative phonology has been the development of frameworks where phonological units are organized in a non-linear fashion. Taking autosegmental phonology (Goldsmith, 1976) as our main exemplar of such frameworks, we wish to address the following question: What is the appropriate interpretation of autosegmental representations? There is, of course, a further question about what we mean by INTERPRETATION: formal, phonetic or computational interpretation? Although we will concentrate on the first of these, we believe that all three aspects should be regarded as closely inter-connected and mutually constraining. The question of interpreting autosegmental representation has in fact been recently posed by Sagey (1988), and we shall take her proposal as our starting point. While it is uncontroversial to suppose that the relationship between units on a given autosegmental tier is one of temporal precedence, Sagey claims that it is more problematic to pin down what is meant by association between tiers. She argues, cogently we believe, that if association is taken to be a relationship of simultaneity between durationless units, then standard analyses of complex segments and gemination lead to logical inconsistency. Instead, association should be taken as temporal OVERLAP between units with duration.

Toward a computational interpretation of situation semantics: Yves Lesperance: Computer Systems Research Institute, University of Toronto, Toronto, April 1986

toward a computational interpretation of situation semantics: Yves Lesperance: Computer Systems Research Institute, University of Toronto, Toronto, April 1986

Electronic structure studies with positrons: a new approach to wavefunction effects

A new approach to the analysis of positron annihilation angular correlation data based on the definition of the LCW folded k-space density in terms of real-space matrix elements and an orbital angular momentum l-based wavefunction expansion is presented and discussed. The computational convenience and interpretation utility of this approach is illustrated with an example calculation for niobium.

Toward a computational interpretation of situation semantics1

Situation semantics proposes novel and attractive treatments for several problem areas of natural language semantics, such as efficiency (context sensitivity) and prepositional attitude reports. Its focus on the information carried by utterances makes the approach very promising for accounting for pragmatic phenomena. However, situation semantics seems to oppose several basic assumptions underlying current approaches to natural language processing and the design of intelligent systems in general. It claims that efficiency undermines the standard notions of logical form, entailment, and proof theory, and objects to the view that mental processes necessarily involve internal representations. The paper attempts to clarify these issues and discusses the impact of situation semantics’ criticisms for natural language processing, knowledge representation, and reasoning. I claim that the representational approach is the only currently practical one for the design of large intelligent systems, but argue that the representations used should be efficient in order to account for the system's embedding in its environment. The paper concludes by stating some constraints that a computational interpretation of situation semantics should obey and discussing remaining problems.

Tests of electric and electromagnetic methods in the travale geothermal field

Within the framework of an EEC project involving ten European laboratories, research on the application of several electric and electromagnetic methods to a geothermal field (Travale, Tuscany), has been undertaken by the B.R.G.M. The objective was to refine the conceptual model of the Travale field and, therefore, to describe the morphology of the basement (down to 2 km depth) and of the Rhaetian reservoir covered by impermeable series. The method best suited to this type of prospection appeared to be electrical dipole — dipole profiling, combined with a 2-D interpretation. Contrasts at more than 2 km depth (500 m long dipoles) could be seen and compared to the depths measured in the boreholes. The EM Melos method (Syscal equipment) should be improved (lower frequencies) to increase the depth penetration. It is, however, a good complementary method for the surface layers. An attempt at a computational interpretation of the self potential profiles gave promising results. To make full advantage of the bipole — dipole measurements efforts should be devoted to their computational interpretation.

A theory of bipolar synchronization schemes

The aim is to better understand the relationships between choice and concurrency that lead to the good behaviour of distributed systems. In order to do so, we formulate a model based on Petri nets and develop its theory. The model is called bipolar synchronization schemes (bp schemes) and the theory we construct is mainly devoted to synthesising, in a systematic fashion, all well behaved bp schemes. We also provide a computational interpretation of well behaved bp schemes. Through this interpretation the insights gained by developing the theory of bp schemes can be transferred to concurrent programs.

A Theory for Bipolar Synchronisation Schemes

The aim is to better understand the relationships between choice and concurrency that lead to the good behaviour of distributed systems. In order to do so, we formulate a model based on Petri nets and develop its theory. The model is called bipolar synchronisation schemes (bp schemes) and the theory we construct is mainly devoted to synthesizing, in a systematic fashion, all well behaved bp schemes. We also provide a computational interpretation of well behaved bp schemes. Through this interpretation the insights gained by developing the theory of bp schemes can be transferred to concurrent programs.

On database systems development through logic

The use of logic as a single tool for formalizing and implementing different aspects of database systems in a uniform manner is discussed. The discussion focuses on relational databases with deductive capabilities and very high-level querying and defining features. The computational interpretation of logic is briefly reviewed, and then several pros and cons concerning the description of data, programs, queries, and language parser in terms of logic programs are examined. The inadequacies are discussed, and it is shown that they can be overcome by the introduction of convenient extensions into logic programming. Finally, an experimental database query system with a natural language front end, implemented in PROLOG, is presented as an illustration of these concepts. A description of the latter from the user's point of view and a sample consultation session in Spanish are included.

New interpretations, anomalous degeneracies, and SO(4) theory for electron correlation in first-row atoms and multiply-excited states

Geometrical and computational interpretations are offered for configuration-mixed ..cap alpha.. (1s/sup d/2s/sup 2/2p/sup m/) + ..beta.. (1s/sup d/2p/sup m/+2) (where d = 0 or 2) valence states based on new profiles of L-shell mixing coefficients, correlation energies, and pair-function angular distributions for both ground and excited states. When viewed for species having the same degree of ionization Z-N, the profiles constructed for the internal and semi-internal ''nondynamical'' correlation energies computed by Sinanoglu's ''non-closed-shell many-electron theory'' are found to display a striking, approximate particle-hole symmetry with respect to total L-shell occupancy. Near-degeneracy-type correlation energy for /sup 3/P and /sup 1/D levels of C-like atoms becomes exactly degenerate when the same radial functions are used for both states. The mixing structure for all L-shell states is described accurately by an N-electron operator ..lambda.. (N) = ..sigma../sub i/< j (A/sub i/-A/sub j/)/sup 2/ with single-particle SO(4) generators A/sub i/ like the Runge-Lenz vector. ..lambda.. (N) represents an approximate ''correlation invariant'' for L-shell mixings.

Reactor Criticality and Nonnegative Matrices

The Perron-Frobenius theory of nonnegative matrices is applied to provide a mathematical basis for the physical concept of criticality and for typical computational interpretations of this concept. (W. L. H.)