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Abstract. Ontologies are a crucial tool for formally specifying the vocabulary and relationship of concepts used on the Semantic Web. In order to share information, agents that use different vocabularies must be able to translate data from one ontological framework to another. Ontology translation is required when translating datasets, generating ontology extensions, and querying through different ontologies. OntoMerge, an online system for ontology merging and automated reasoning, can implement ontology translation with inputs and outputs in OWL or other web languages. The merge of two related ontologies is obtained by taking the union of the concepts and the axioms defining them, and then adding bridging axioms that relate their concepts. The resulting merged ontology then serves as an inferential medium within which translation can occur. Our internal representation, Web-PDDL, is a strong typed first-order logic language for web application. Using a uniform notation for all problems allows us to factor out syntactic and semantic translation problems, and focus on the latter. Syntactic translation is done by an automatic translator between Web-PDDL and OWL or other web languages. Semantic translation is implemented using an inference engine (OntoEngine) which processes assertions and queries in Web-PDDL syntax, running in either a data-driven (forward chaining) or demand-driven (backward chaining) way. 1

Introduction Many researchers who study the theoretical aspects of inference systems believe that if inference rule A is complete and more restrictive than inference rule B, then the use of A will lead more quickly to proofs than will the use of B. The literature contains statements of the sort "our rule is complete and it heavily prunes the search space; therefore it is efficient". 2 These positions are highly questionable and indicate that the authors have little or no experience with the practical use of automated inference systems. Restrictive rules (1) can block short, easy-to-find proofs, (2) can block proofs involving simple clauses, the type of clause on which many practical searches focus, (3) can require weakening of redundancy control such as subsumption and demodulation, and (4) can require the use of complex checks in deciding whether such rules should be applied. The only way to determ

The aim of this work is the development and application of a partial evaluation procedure for rewriting-based functional logic programs. Functional logic programming languages unite the two main declarative programming paradigms. The rewriting-based computational model extends traditional functional programming languages by incorporating logical features, including logical variables and built-in search, into its framework. This work is the first to address the automatic specialisation of these functional logic programs. In particular, a theoretical framework for the partial evaluation of rewriting-based functional logic programs is defined and its correctness is established. Then, an algorithm is formalised which incorporates the theoretical framework for the procedure in a fully automatic technique. Constraint solving is used to represent additional information about the terms encountered during the transformation in order to improve the efficiency and size of the residual programs. ...

In mathematics there exist powerful symbolic computation packages which have drawn considerable attention, also because of their easy-to-use interfaces and graphical capabilities. In computer logic, however, there were mainly complex tools for experts or purely didactic proof assistants. The Logics Workbench LWB is an attempt to fill this gap in the area of propositional logics. On the one hand, the LWB is intended for being used as an educational tool, especially for non-classical logics, and on the other hand as a programmable logic platform for more experienced users. The present thesis comprises three major parts: a system design, an empirical study, and a theoretical contribution. (a) Beside a general introduction to the LWB, we will present design aspects of its key components in the first part: the kernel, the parser, the programming language and the user interface. It is shown that the adopted solutions are adequate for doing logic on the computer. The design goal is to provid...

Experimentation strongly suggests that, for attacking deep questions and hard problems with the assistance of an automated reasoning program, the more effective paradigms rely on the retention of deduced information. A significant obstacle ordinarily presented by such a paradigm is the deduction and retention of one or more needed conclusions whose complexity sharply delays their consideration. To mitigate the severity of the cited obstacle, I formulated and feature in this article the hot list strategy. The hot list strategy asks the researcher to choose, usually from among the input statements characterizing the problem under study, one or more statements that are conjectured to play a key role for assignment completion. The chosen statements---conjectured to merit revisiting, again and again---are placed in an input list of statements, called the hot list. When an automated reasoning program has decided to retain a new conclusion C---before any other statement is chosen to initiat...

For more than three and one-half decades beginning in the early 1960s, a heavy emphasis on proof finding has been a key component of the Argonne paradigm, whose use has directly led to significant advances in automated reasoning and important contributions to mathematics and logic. The theorems that have served well range from the trivial to the deep, even including some that corresponded to open questions. Often the paradigm asks for a theorem whose proof is in hand but that cannot be obtained in a fully automated manner by the program in use. The theorem whose hypothesis consists solely of the Meredith single axiom for two-valued sentential (or propositional) calculus and whose conclusion is the Lukasiewicz three-axiom system for that area of formal logic was just such a theorem. Featured in this article is the methodology that enabled the program OTTER to find the first fully automated proof of the cited theorem, a proof with the intriguing property that none of its steps...

ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semi-simple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...

This paper shows on a non-trivial example that it is possible to mix proving and computing using current technologies. We present a proof of the Buchberger's algorithm that has been developed in the Coq proof assistant. The formulation of the algorithm in Coq can then be efficiently compiled and used to do computation.

Machine [War83] implementation for Prolog) are stored in an array similar to the WAM heap. It is an array of pairs h tag, address i, where tag can be ref or struct, that is, a function symbol f. The field address contains a heap address. Terms are stored on the heap as in the WAM: each function symbol of arity n is followed by n contiguous ref positions pointing to its arguments. Each uninstantiated variable corresponds to a ref position pointing to itself. For example, the heap below at the left contains f(x; g(x); g(x); y) at the address 20: . . . . . . 20 f 21 ref 21 22 ref 30 23 ref 30 24 ref 24 . . . . . . 30 g 31 ref 21 . . . . . . Note that in such a representation the whole term needs not to be contiguous, and that common subterms ---not only variables--- can be shared, like the subterm g(x) at position 30. Moreover, unlike it happens in other term representations, matching and unification operations do not need to deal with a partial substitution: du...