107,797 research outputs found
Goal driven theorem proving using conceptual graphs and Peirce logic
The thesis describes a rational reconstruction of Sowa's theory of Conceptual
Graphs. The reconstruction produces a theory with a firmer logical foundation than was
previously the case and which is suitable for computation whilst retaining the
expressiveness of the original theory. Also, several areas of incompleteness are
addressed. These mainly concern the scope of operations on conceptual graphs of
different types but include extensions for logics of higher orders than first order. An
important innovation is the placing of negation onto a sound representational basis.
A comparison of theorem proving techniques is made from which the principles of
theorem proving in Peirce logic are identified. As a result, a set of derived inference rules,
suitable for a goal driven approach to theorem proving, is developed from Peirce's beta
rules. These derived rules, the first of their kind for Peirce logic and conceptual graphs,
allow the development of a novel theorem proving approach which has some similarities
to a combined semantic tableau and resolution methodology. With this methodology it is
shown that a logically complete yet tractable system is possible. An important result is the
identification of domain independent heuristics which follow directly from the
methodology. In addition to the theorem prover, an efficient system for the detection of
selectional constraint violations is developed.
The proof techniques are used to build a working knowledge base system in Prolog
which can accept arbitrary statements represented by conceptual graphs and test their
semantic and logical consistency against a dynamic knowledge base. The same proof
techniques are used to find solutions to arbitrary queries. Since the system is logically
complete it can maintain the integrity of its knowledge base and answer queries in a fully
automated manner. Thus the system is completely declarative and does not require any
programming whatever by a user with the result that all interaction with a user is
conversational. Finally, the system is compared with other theorem proving systems
which are based upon Conceptual Graphs and conclusions about the effectiveness of the
methodology are drawn
Loop elimination, a sound optimisation technique for PTTP related theorem proving
In this paper we present loop elimination, an important optimisation technique for first-order theorem proving based on Prolog technology, such as the Prolog Technology Theorem Prover or the DLog Description Logic Reasoner. Although several loop checking techniques exist for logic programs, to the best of our knowledge, we are the first to examine the interaction of loop checking with ancestor resolution. Our main contribution is a rigorous proof of the soundness of loop elimination
Inductive Theorem Proving Using Refined Unfailing Completion Techniques
We present a brief overview on completion based inductive theorem proving techniques, point out the key concepts for the underlying "proof by consistency" - paradigm and isolate an abstract description of what is necessary for an algorithmic realization of such methods.
In particular, we give several versions of proof orderings, which - under certain conditions - are well-suited for that purpose. Together with corresponding notions of (positive and negative) covering sets we get abstract "positive" and "negative" characterizations of inductive validity. As a consequence we can generalize known criteria for inductive validity, even for the cases where some of the conjectures may not be orientable or where the base system is terminating but not necessarily ground confluent.
Furthermore we consider several refinements and optimizations of completion based inductive theorem proving techniques. In particular, sufficient criteria for being a covering set including restrictions of critical pairs (and the usage of non-equational inductive knowledge) are discussed.
Moreover a couple of lemma generation methods are briefly summarized and classified. A new techniques of save generalization is particularly interesting, since it provides means for syntactic generalizations, i.e. simplifications, of conjectures without loosing semantic equivalence.
Finally we present the main features and characteristics of UNICOM, an inductive theorem prover with refined unfailing completion techniques and built on top of TRSPEC, a term rewriting based system for investigating algebraic specifications
Matrix proof method in annotated paraconsistent logic
The matrix connection method (MCM) is an alternative procedure for theorem proving than the usual resolution technique. We already have used the MCM for finding models in a real-time knowledge-based system generator. In this paper, we adapt the MCM to the particular case of sorne annotated propositional paraconsistent logics. Further developments related to these ideas are also outlined.Eje: 2do. Workshop sobre aspectos teóricos de la inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI
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