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not be interpreted as representing the o cial policies, either expressed or implied, of NSF or the U.S. Government. This thesis describes the design of a meta-logical framework that supports the representation and veri cation of deductive systems, its implementation as an automated theorem prover, and experimental results related to the areas of programming languages, type theory, and logics. Design: The meta-logical framework extends the logical framework LF [HHP93] by a meta-logic M + 2. This design is novel and unique since it allows higher-order encodings of deductive systems and induction principles to coexist. On the one hand, higher-order representation techniques lead to concise and direct encodings of programming languages and logic calculi. Inductive de nitions on the other hand allow the formalization of properties about deductive systems, such as the proof that an operational semantics preserves types or the proof that a logic is is a proof calculus whose proof terms are recursive functions that may be consistent.M +

We present an automated abstract verification method for infinite-state systems specified by logic programs (which are a uniform and intermediate layer to which diverse formalisms such as transition systems, pushdown processes and while programs can be mapped). We establish connections between: logic program semantics and CTL properties, set-based program analysis and pushdown processes, and also between model checking and constraint solving, viz. theorem proving. We show that set-based analysis can be used to compute supersets of the values of program variables in the states that satisfy a given CTL property.

This paper reports on an empirical performance analysis of four modal theorem provers on benchmark suites of randomly generated formulae. The theorem provers tested are the Davis-Putnam-based procedure Ksat, the tableaux-based system KRIS, the sequent-based Logics Workbench, and a translation approach combined with the first-order theorem prover SPASS.

Real-world applications of automated theorem proving require modern software environments that enable modularisation, networked inter-operability, robustness, and scalability. These requirements are met by the Agent-Oriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...

. We follow the set-based approach to directional types proposed by Aiken and Lakshman [1]. Their type checking algorithm works via set constraint solving and is sound and complete for given discriminative types. We characterize directional types in model-theoretic terms. We present an algorithm for inferring directional types. The directional type that we derive from a logic program P is uniformly at least as precise as any discriminative directional type of P, i.e., any directional type out of the class for which the type checking algorithm of Aiken and Lakshman is sound and complete. We improve their algorithm as well as their lower bound and thereby settle the complexity (DEXPTIME-complete) of the corresponding problem. 1 Introduction Directional types form a type system for logic programs which is based on the view of a predicate as a directional procedure which, when applied to a tuple of input terms, generates a tuple of output terms. There is a rich literature on ty...

.24> existential and universal role restriction operations: some and all, as well as domain and range, ffl additional role operators: comp (composition), sum (relative sum), conv (converse), id (identity), div (diversity) , and ffl test (test), domrestr (domain restriction) and ranrestr (range restriction). mspass supports terminological axioms in their most general form, which includes generalised inclusion and equivalence axioms, for both concepts and roles. In addition, because the first-order symbol associated by the translation mapping to a propositional symbol can be declared, it is possible to specify ABox statements as well as any first-order restrictions on concepts and roles. Translation mappings A number of different translatio

We show that unification in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories. We show that saturation under sorted superposition is effective on sorted shallow equational theories. So called semi-linear equational theories can be e ectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.

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This thesis studies the optimised functional translation of propositional modal logics to first-order logic, and first-order resolution as a means for realising modal reasoning. The optimised functional translation maps modal logics to a lattice of clausal logics, called path logics. The general apparatus of inference for path logics is theory resolution. We show that satisfiability in basic path logic and certain extensions can be decided by resolution and condensing without requiring additional refinement strategies. We propose an improved theory unification algorithm for S4, and we present a calculus of ordered E-resolution with normalisation. We show also that some essentially second-order modal logics convert to path logics, which can be exploited for accomodating inference for modal logics with numerical quantifiers in a calculus of resolution and simple arithmetic. Zusammenfassung Diese Arbeit untersucht die optimierte funktionale Ubersetzung von modalen Aussagenlogiken in die...