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25
OMDoc: An Open Markup Format for Mathematical Documents
, 2000
"... In this report we present an extension OMDoc to the OpenMath standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematic ..."
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Cited by 183 (44 self)
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In this report we present an extension OMDoc to the OpenMath standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematical services on a mathematical software bus. We motivate and describe the OMDoc language and present an Xml document type definition for it. Furthermore, we discuss applications and tool support.
Strategies for Temporal Resolution
, 1995
"... Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algo ..."
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Cited by 114 (47 self)
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Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algorithms for, and strategies to guide, a fully automated temporal resolution theorem prover are given, proved correct and evaluated. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states and temporal resolution over states. It has only one temporal resolution rule and is therefore particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, different algorithms on w...
Automating the Meta Theory of Deductive Systems
, 2000
"... 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 metalogical framework that supports the representation and veri cation of deductive systems, its implementation as an automated theorem prover, a ..."
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Cited by 88 (16 self)
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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 metalogical 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 metalogical framework extends the logical framework LF [HHP93] by a metalogic M + 2. This design is novel and unique since it allows higherorder encodings of deductive systems and induction principles to coexist. On the one hand, higherorder 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 +
Setbased Analysis of Reactive Infinitestate Systems
, 1997
"... We present an automated abstract verification method for infinitestate 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: logi ..."
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Cited by 27 (8 self)
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We present an automated abstract verification method for infinitestate 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, setbased program analysis and pushdown processes, and also between model checking and constraint solving, viz. theorem proving. We show that setbased analysis can be used to compute supersets of the values of program variables in the states that satisfy a given CTL property.
An Empirical Analysis Of Modal Theorem Provers
"... 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 DavisPutnambased procedure Ksat, the tableauxbased system KRIS, the sequentbased Logics Workbench, and a translation appro ..."
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Cited by 26 (10 self)
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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 DavisPutnambased procedure Ksat, the tableauxbased system KRIS, the sequentbased Logics Workbench, and a translation approach combined with the firstorder theorem prover SPASS.
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 20 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented 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...
Directional Type Inference for Logic Programs
, 1998
"... . We follow the setbased 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 modeltheoretic terms. We present an algorithm ..."
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Cited by 16 (6 self)
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. We follow the setbased 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 modeltheoretic 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 (DEXPTIMEcomplete) 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...
Detecting Unsolvable Queries for Definite Logic Programs
, 1998
"... In logic programming, almost no work has been done so far on proving that certain queries cannot succeed. Work in this direction could be useful for queries which seem to be nonterminating. Such queries are not exceptional, e.g. in planning problems. The paper develops some methods, based on ab ..."
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Cited by 11 (3 self)
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In logic programming, almost no work has been done so far on proving that certain queries cannot succeed. Work in this direction could be useful for queries which seem to be nonterminating. Such queries are not exceptional, e.g. in planning problems. The paper develops some methods, based on abduction, goaldirectedness, tabulation, and constraint techniques, for proving failure of queries for definite logic programs. It also reports some experiments with various tools.
Optimised Modal Translation and Resolution
, 1997
"... This thesis studies the optimised functional translation of propositional modal logics to firstorder logic, and firstorder 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 app ..."
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Cited by 11 (2 self)
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This thesis studies the optimised functional translation of propositional modal logics to firstorder logic, and firstorder 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 Eresolution with normalisation. We show also that some essentially secondorder 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...