Syntactic Computation as Labelled Deduction: WH a case study

This paper addresses the question "Why do WH phenomena occur with the particular cluster of properties observed across languages -- long-distance dependencies, WH-in situ, partial movement constructions, reconstruction, crossover etc." These phenomena have been analysed by invoking a number of discrete principles and categories, but have so far resisted a unified treatment. The explanation proposed is set within a model of natural language understanding in context, where the task of understanding is taken to be the incremental building of a structure over which the semantic content is defined. The formal model is a composite of a labelled type-deduction system, a modal tree logic, and a set of rules for describing the process of interpreting the string as a set of transition states. A dynamic concept of syntax results, in which in addition to an output structure associated with each string (analogous to the level of LF), there is in addition an explicit meta-level description of the process whereby this incremental process takes place. This paper argues that WH-related phenomena can be unified by adopting this dynamic perspective. The main focus of the paper is on WH-initial structures, WH in situ structures, partial movement phenomena, and crossover phenomena. In each case, an analysis is proposed which emerges from the general characterisatioan of WH structures without construction-specific stipulation.Articl

Evaluation of Datalog queries and its application to the static analysis of Java code

Two approaches for evaluating Datalog programs are presented: one based on boolean equation systems, and the other based on rewriting logic. The work is presented in the context of the static analysis of Java programs specified in Datalog.Feliú Gabaldón, MA. (2010). Evaluation of Datalog queries and its application to the static analysis of Java code. http://hdl.handle.net/10251/14016Archivo delegad

Abella: A System for Reasoning about Relational Specifications

International audienceThe Abella interactive theorem prover is based on an intuitionistic logic that allows for inductive and co-inductive reasoning over relations. Abella supports the λ-tree approach to treating syntax containing binders: it allows simply typed λ-terms to be used to represent such syntax and it provides higher-order (pattern) unification, the ∇ quantifier, and nominal constants for reasoning about these representations. As such, it is a suitable vehicle for formalizing the meta-theory of formal systems such as logics and programming languages. This tutorial exposes Abella incrementally, starting with its capabilities at a first-order logic level and gradually presenting more sophisticated features, ending with the support it offers to the two-level logic approach to meta-theoretic reasoning. Along the way, we show how Abella can be used prove theorems involving natural numbers, lists, and automata, as well as involving typed and untyped λ-calculi and the π-calculus

Logic-based techniques for program analysis and specification synthesis

La Tesis investiga técnicas ágiles dentro del paradigma declarativo para dar solución a dos problemas: el análisis de programas y la inferencia de especificaciones a partir de programas escritos en lenguajes multiparadigma y en lenguajes imperativos con tipos, objetos, estructuras y punteros. Respecto al estado actual de la tesis, la parte de análisis de programas ya está consolidada, mientras que la parte de inferencia de especificaciones sigue en fase de desarrollo activo. La primera parte da soluciones para la ejecución de análisis de punteros especificados en Datalog. En esta parte se han desarrollado dos técnicas de ejecución de especificaciones en dicho lenguaje Datalog: una de ellas utiliza resolutores de sistemas de ecuaciones booleanas, y la otra utiliza la lógica de reescritura implementada eficientemente en el lenguaje Maude. La segunda parte desarrolla técnicas de inferencia de especificaciones a partir de programas. En esta parte se han desarrollado dos métodos de inferencia de especificaciones. El primer método se desarrolló para el lenguaje lógico-funcional Curry y permite inferir especificaciones ecuacionales mediante interpretación abstracta de los programas. El segundo método está siendo desarrollado para lenguajes imperativos realistas, y se ha aplicado a un subconjunto del lenguaje de programación C. Este método permite inferir especificaciones en forma de reglas que representan las distintas relaciones entre las propiedades que el estado de un programa satisface antes y después de su ejecución. Además, estas propiedades son expresables en términos de las abstracciones funcionales del propio programa, resultando en una especificación de muy alto nivel y, por lo tanto, de más fácil comprensión.Feliú Gabaldón, MA. (2013). Logic-based techniques for program analysis and specification synthesis [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/33747TESI

Verifying temporal properties using explicit approximants: completeness for context-free processes

We present a sequent calculus for formally verifying modal -calculus properties of concurrent processes. Building on work by Dam and Gurov, the proof system contains rules for the explicit manipulation of fixed-point approximants. We develop a new syntax for approximants, incorporating, in particular, a mechanism for approximant modification. We make essential use of this feature to prove our main result: the sequent calculus is complete for establishing arbitrary -calculus properties of context-free processes

The efficient evaluation of visual queries within a logic-based framework

Bibliography: leaves 149-153.There has been much research in the area of visual query systems in recent years. This has stemmed from the need for a more powerful database visualization and querying ability. In addition, there has been a pressing need for a more intuitive interface for the non-expert user. Systems such as Hy+, developed at the University of Toronto, provide environments that satisfy a wide range of database interaction and querying, with the advantage of maintaining a visual interface abstraction throughout. This thesis explores issues related to the translation and evaluation of visual queries, including semantic and optimization possibilities. The primary focus will be on the GraphLog query language, defined in the context of the Hy+ visualization system. GraphLog is translated to the deductive database language Datalog, which is subsequently evaluated by the CORAL logic database system. We propose graph semantics, which define the meaning of visual queries in terms of paths in a graph, for monotone GraphLog. This provides a more intuitive meaning which is not linked to any particular translation. Therefore, Datalog generated by a translation may be compared to well-defined semantics to ensure that the translation preserves the intended meaning. By examining various queries in terms of the graph semantics, we uncover a shortcoming in the existing GraphLog translation. In addition, an alternative translation to Datalog, based on the construction of a nondeterministic finite state automaton, is described for GraphLog queries. The translation has the property that visual queries containing constants are optimized using a technique known as factoring. In addition, the translation performs an optimization on queries with multiple edges that contain no constants, referred to here as variable constraining

Reasoning About Strategies: On the Model-Checking Problem

In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL\star, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHP-SL, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the very specific setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems. In this paper, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multi-agent concurrent games. We prove that SL includes CHP-SL, while maintaining a decidable model-checking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHP-SL. Moreover, we prove that such a problem for SL is NonElementarySpace-hard. This negative result has spurred us to investigate here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of obtaining an elementary model-checking problem. Among the others, we study the sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, a single goal at a time. About these logics, we prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not harder than the one for ATL\star

The use of proof plans in tactic synthesis

We undertake a programme of tactic synthesis. We first formalize the notion of a tactic as a rewrite rule, then give a correctness criterion for this by means of a reflection mechanism in the constructive type theory OYSTER. We further formalize the notion of a tactic specification, given as a synthesis goal and a decidability goal. We use a proof planner. CIAM. to guide the search for inductive proofs of these, and are able to successfully synthesize several tactics in this fashion. This involves two extensions to existing methods: context-sensitive rewriting and higher-order wave rules. Further, we show that from a proof of the decidability goal one may compile to a Prolog program a pseudo- tactic which may be run to efficiently simulate the input/output behaviour of the synthetic tacti