A Framework for the Flexible Integration of a Class of Decision Procedures into Theorem Provers

The role of decision procedures is often essential in theorem proving. Decision procedures can reduce the search space of heuristic components of a prover and increase its abilities. However, in some applications only a small number of conjectures fall within the scope of the available decision procedures. Some of these conjectures could in an informal sense fall ‘just outside’ that scope. In these situations a problem arises because lemmas have to be invoked or the decision procedure has to communicate with the heuristic component of a theorem prover. This problem is also related to the general problem of how to exibly integrate decision procedures into heuristic theorem provers. In this paper we address such problems and describe a framework for the exible integration of decision procedures into other proof methods. The proposed framework can be used in different theorem provers, for different theories and for different decision procedures. New decision procedures can be simply ‘plugged-in’ to the system. As an illustration, we describe an instantiation of this framework within the Clam proof-planning system, to which it is well suited. We report on some results using this implementation

Strategies for conformance testing

A new test generation method and algorithm for conformance testing is proposed. It is based on the interpretation of testing concepts from the ISO standard ``Formal methods in conformance testing'' in a game theory setting. A testing game is defined with a specification given as an Input/Output State Machine and a test purpose for test selection. A winning strategy for this game define a tester for a class of implementations and a conformance relation. \begin{keywords} formal methods in conformance testing, test purposes, games strategies, test assumptions, input-output state machines. \end{keywords

E-unification for subsystems of S4

This paper is concerned with the unification problem in the path logics associated by the optimised functional translation method with the propositional modal logics \textit{K}, \textit{KD}, \textit{KT}, \textit{KD4}, \textit{S4} and \textit{S5}. It presents improved unification algorithms for certain forms of the right identity and associativity laws. The algorithms employ mutation rules, which have the advantage that terms are worked off from the outside inward, making paramodulating into terms superfluous

How generic language extensions enable ''open-world'' design in Java

By \emph{open--world design} we mean that collaborating classes are so loosely coupled that changes in one class do not propagate to the other classes, and single classes can be isolated and integrated in other contexts. Of course, this is what maintainability and reusability is all about. In the paper, we will demonstrate that in Java even an open--world design of mere attribute access can only be achieved if static safety is sacrificed, and that this conflict is unresolvable \emph{even if the attribute type is fixed}. With generic language extensions such as GJ, which is a generic extension of Java, it is possible to combine static type safety and open--world design. As a consequence, genericity should be viewed as a first--class design feature, because generic language features are preferably applied in many situations in which object--orientedness seems appropriate. We chose Java as the base of the discussion because Java is commonly known and several advanced features of Java aim at a loose coupling of classes. In particular, the paper is intended to make a strong point in favor of generic extensions of Java

Model checking infinite-state systems in CLP

The verification of safety and liveness properties for infinite-state systems is an important research problem. Can the well-established concepts and the existing technology for programming over constraints as first-class data structures contribute to this research? The work reported in this paper is a starting point for the experimental evaluation of constraint logic programming as a conceptual basis and practical implementation platform for model checking. We have implemented an automated verification method in CLP using real and boolean constraints. We have used the method on a number of infinite-state systems that model concurrent programs using integers or buffers. The basis of the correctness of our implementation is a formal connection between CLP programs and the formalism used for specifying concurrent systems

Symmetries in logic programs

We investigate the structures and above all, the applications of a class of symmetric groups induced by logic programs. After establishing the relationships between minimal models of logic programs and their simplified forms, and models of their completions, we show that in general when deriving negative information, we can apply the CWA, the GCWA, and the completion procedure directly from some simplified forms of the original logic programs. The least models and the results of SLD-resolution stay invariant for definite logic programs and their simplified forms. The results of SLDNF-resolution, the standard or perfect models stay invariant for hierarchical, stratified logic programs and some of their simplified forms, respectively. We introduce a new proposal to derive negative information termed OCWA, as well as the new concepts of quasi-definite, quasi-hierarchical and quasi-stratified logic programs. We also propose semantics for them

The most nonelementary theory (a direct lower bound proof)

We give a direct proof by generic reduction that a decidable rudimentary theory of finite typed sets [Henkin 63, Meyer 74, Statman 79, Mairson 92] requires space exceeding infinitely often an exponentially growing stack of twos. This gives the highest currently known lower bound for a decidable logical theory and affirmatively answers to Problem 10.13 of [Compton & Henson 90]: Is there a `natural' decidable theory with a lower bound of the form $\exp_\infty(f(n))$, where $f$ is not linearly bounded? The highest previously known lower and upper bounds for `natural' decidable theories, like WS1S, S2S, are `just' linearly growing stacks of twos

The undecidability of the first-order theories of one step rewriting in linear canonical systems

By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the EAAA-theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable EA...A-theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind