On structuring proof search for first order linear logic

Full first-order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the ‘proof search as computation’ paradigm. However, Forum still has to deal with syntactic details that would normally be ignored by a reasonable operational semantics. In this respect, Forum improves on Gentzen systems for linear logic by restricting the language and the form of inference rules. We further improve on Forum by restricting the class of formulae allowed, in a system we call G-Forum, which is still equivalent to full first-order linear logic. The only formulae allowed in G-Forum have the same shape as Forum sequents: the restriction does not diminish expressiveness and makes G-Forum amenable to proof theoretic analysis. G-Forum consists of two (big) inference rules, for which we show a cut elimination procedure. This does not need to appeal to finer detail in formulae and sequents than is provided by G-Forum, thus successfully testing the internal symmetries of our system.     

Hierarchies of modal and temporal logics with reference pointers

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions.     

TABLEAUX: A general theorem prover for modal logics

We present a general theorem proving system for propositional modal logics, called TABLEAUX. The main feature of the system is its generality, since it provides an unified environment for various kinds of modal operators and for a wide class of modal logics, including usual temporal, epistemic or dynamic logics. We survey the modal languages covered by TABLEAUX, which range from the basic one L(, ) through a complex multimodal language including several families of operators with their transitive-closure and converse. The decision procedure we use is basically a semantic tableaux method, but with slight modifications compared to the traditional one. We emphasize the advantages of such semantical proof methods for modal logics, since we believe that the models construction they provide represents perhaps the most attractive feature of these logics for possible applications in computer science and AI. The system has been implemented in Prolog, and appears to be of reasonable efficiency for most current examples. Experimental results are given in the paper, with two lists of test examples.A preliminary version of this paper appeared in the Proceedings of the International Computer Science Conference (ICSC'88), Hong-Kong, December 19–21, 1988.     

An institution of modal logics for coalgebras

This paper presents a modular framework for the specification of certain inductively-defined coalgebraic types. Modal logics for coalgebras of polynomial endofunctors on the category of sets have been studied in [M. Rößiger, Coalgebras and modal logic, in: H. Reichel (Ed.), Coalgebraic Methods in Computer Science, Electronic Notes in Theoretical Computer Science, vol. 33, Elsevier Science, 2000, pp. 299–320; B. Jacobs, Many-sorted coalgebraic modal logic: a model-theoretic study, Theoretical Informatics and Applications 35(1) (2001) 31–59]. These logics are here generalised to endofunctors on categories of sorted sets, in order to allow collections of inter-related types to be specified simultaneously. The inductive nature of the coalgebraic types considered is then used to formalise semantic relationships between different types, and to define translations between the associated logics. The resulting logical framework is shown to be an institution, whose specifications and specification morphisms admit final and respectively cofree models.     

A construction of one-point bases in extended lambda calculi

We present a general schema for constructing infinitely-many one-point bases for -calculi extended by finitely-many constants. The constants are usually present in programming languages, and may involve reduction rules other than β-reduction. The construction can be implemented in a functional subset of LISP/Scheme, giving one-point bases for applicative-order calculi extended by constants from the underlying programming language.     

Interpretability of first-order linear temporal logics in fork algebras

In this paper we prove theorems on the interpretability of the first-order temporal logics LTL and TL into Fork Algebras. This result is part of a research project on the interpretability of logics in Fork Algebras, and has important applications towards the relational specification of properties of systems within the Ar_gentum tool.     

A polynomial space construction of tree-like models for logics with local chains of modal connectives

The LA-logics (“logics with Local Agreement”) are polymodal logics defined semantically such that at any world of a model, the sets of successors for the different accessibility relations can be linearly ordered and the accessibility relations are equivalence relations. In a previous work, we have shown that every LA-logic defined with a finite set of modal indices has an NP-complete satisfiability problem. In this paper, we introduce a class of LA-logics with a countably infinite set of modal indices and we show that the satisfiability problem is PSPACE-complete for every logic of such a class. The upper bound is shown by exhibiting a tree structure of the models. This allows us to establish a surprising correspondence between the modal depth of formulae and the number of occurrences of distinct modal connectives. More importantly, as a consequence, we can show the PSPACE-completeness of Gargov's logic DALLA and Nakamura's logic LGM restricted to modal indices that are rational numbers, for which the computational complexity characterization has been open until now. These logics are known to belong to the class of information logics and fuzzy modal logics, respectively.     

描述逻辑的动态时序扩展*

在一些基于本体的动态应用中,需要描述组合动作和变化域的时间特性。为了对这类应用建模,通过整合动态时序逻辑和描述逻辑,提出一类描述逻辑扩展。分析了该类扩展的基本形式DLTLALC的语法和语义,并提出一种可终止的tableau算法判别DLTLALC公式可满足性。利用该类扩展,可以表达组合动作执行过程中域变化的时间特性,该类扩展为语义Web服务等动态应用建模和推理提供了一条有效途径。     

An investigation of modal structures as an alternative semantic basis for epistemic logics

In the past, Kripke structures have been used to specify the semantic theory of various modal logics. More recently, modal structures have been developed as an alternative to Kripke structures for providing the semantics of such logics. While these approaches are equivalent in a certain sense, it has been argued that modal structures provide a more appropriate basis for representing the modal notions of knowledge and belief. Since these notions, rather than the traditional notions of necessity and possibility, are of particular interest to artificial intelligence, it is of interest to examine the applicability and versatility of these structures. This paper presents an investigation of modal structures by examining how they may be extended to account for generalizations of Kripke structures. To begin with, we present an alternative formulation of modal structures in terms of trees; this formulation emphasizes the relation between Kripke structures and modal structures, by showing how the latter may be obtained from the former by means of a three-step transformation. Following this, we show how modal structures may be extended to represent generalizations of possible worlds, and to represent generalizations of accessibility between possible worlds. Lastly, we show how modal structures may be used in the case of a full first-order system. In all cases, the extensions are shown to be equivalent to the corresponding extension of Kripke structures.     

Development of a sensor for surface state measurements using experimental and numerical modal analysis

The characterization of the surface state becomes an increasing necessity for many industries. This paper presents a patented measurement method [M.A. Bueno, S. Fontaine, M. Renner, Dispositif Pour Évaluer L’état de Surface d’un Matériau et Procédé de Mise en œuvre Dudit Dispositif, Patent No. PCT/FR01/01770, 2000], which is able to evaluate the surface state of materials. This method gives roughness–friction criteria and is based on the principle of a tribometer of type “blade-disc”, where the analysed surface is the disc. The sensor is an active element, which vibrates according to its vibrating modes. This work shows how experimental and numerical analysis has allowed optimizing its gage instrumentation and its geometry. Moreover, the modal analysis and the building of a numerical model have set up the coupling between mechanical solicitations of the tested surface and mechanical responses of the sensor in each mode. Finally, an example of measurement of known surfaces is illustrated to explain the results of this study and the efficiency of this measurement method.     

The Complexity of Modellability in Finite and Computable Signatures of a Constraint Logic for Head-Driven Phrase Structure Grammar

The SRL (speciate re-entrant logic) of King (1989) is a sound, complete and decidable logic designed specifically to support formalisms for the HPSG (head-driven phrase structure grammar) of Pollard and Sag (1994). The SRL notion of modellability in a signature is particularly important for HPSG, and the present paper modifies an elegant method due to Blackburn and Spaan (1993) in order to prove that

Systematic design of distributed piezoelectric modal sensors/actuators for rectangular plates by optimizing the polarization profile

In this paper the problem of finding the shape of distributed piezoelectric modal sensors/actuators for plates with arbitrary boundary conditions is treated by an optimization approach. A binary function is used to model the design variable: the polarization profile of the piezoelectric layers. Contrary to what it could be expected, it is analytically proved that it is possible to find manufacturable polarization profiles taking on only two values, i.e. either positive or negative polarization. Several numerical examples are shown to corroborate that such topologies isolate particular vibration modes in the frequency domain.     

The density of truth in monadic fragments of some intermediate logics

This paper is an attempt to count the proportion of tautologies of some intermediate logics among all formulas. Our interest concentrates especially on Medvedev’s logic and its fragment over language with one propositional variable.     

A comparison of three uncertainty calculi for building sonar-based occupancy grids

In this paper, we describe and compare three different uncertainty calculi techniques to build occupancy grids of an unknown environment using sensory information provided by a ring of ultrasonic range-finders. These techniques are based on Bayesian theory, Dempster–Shafer theory of evidence, and fuzzy set theory. Several sensor models are presented to handle uncertainty according to the selected building procedure. Experimental examples of occupancy grids, built from real data recorded by two different mobile robots in office-like environment, are presented to perform a comparison among the proposed calculi techniques. Probabilistic and evidence theoretic methods are more accurate in structured environments, while in cases of multiple reflections only the possibilistic approach provides correct results.