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34
The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
NORA/HAMMR: Making DeductionBased Software Component Retrieval Practical
, 1997
"... Deductionbased software component retrieval uses preand postconditions as indexes and search keys and an automated theorem prover (ATP) to check whether a component matches. This idea is very simple but the vast number of arising proof tasks makes a practical implementation very hard. We thus pass ..."
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Cited by 39 (4 self)
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Deductionbased software component retrieval uses preand postconditions as indexes and search keys and an automated theorem prover (ATP) to check whether a component matches. This idea is very simple but the vast number of arising proof tasks makes a practical implementation very hard. We thus pass the components through a chain of filters of increasing deductive power. In this chain, rejection filters based on signature matching and model checking techniques are used to rule out nonmatches as early as possible and to prevent the subsequent ATP from "drowning." Hence, intermediate results of reasonable precision are available at (almost) any time of the retrieval process. The final ATP step then works as a confirmation filter to lift the precision of the answer set. We implemented a chain which runs fully automatically and uses MACE for model checking and the automated prover SETHEO as confirmation filter. We evaluated the system over a mediumsized collection of components. The resul...
Integrating Automated and Interactive Theorem Proving
, 1998
"... Machine code ((Schellhorn and Ahrendt, 1997) and Chapter III.2.6). We use it as a reference or benchmark. Parts of it are repeated every now and then to evaluate the success of our integration concepts, see Section 7. In realistic applications in software verification, proof attempts are more likel ..."
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Cited by 31 (8 self)
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Machine code ((Schellhorn and Ahrendt, 1997) and Chapter III.2.6). We use it as a reference or benchmark. Parts of it are repeated every now and then to evaluate the success of our integration concepts, see Section 7. In realistic applications in software verification, proof attempts are more likely to fail than to go through. This is because specifications, programs, I_3_16mod_a.tex; 9/03/1998; 13:09; p.2 INTEGRATED THEOREM PROVING 549 or userdefined lemmas typically are erroneous. Correct versions usually are only obtained after a number of corrections and failed proof attempts. Therefore, the question is not only how to produce powerful theorem provers but also how to integrate proving and error correction. Current research on this and related topics is discussed in Section 8. There are different approaches of combining interactive methods with automated ones. Their relation to our approach is the subject of Section 9. Finally, in Section 10 we draw conclusions. 2. IDENTIFYING ...
Model Elimination without Contrapositives
, 1994
"... We present modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known pro ..."
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Cited by 16 (6 self)
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We present modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified problem reduction format and NearHorn Prolog.
Spatial Agents Implemented in a Logical Expressible Language
 RoboCup99: Robot Soccer WorldCup III, LNAI 1856
, 1999
"... In this paper, we present a multilayered architecture for spatial and temporal agents. The focus is laid on the declarativity of the approach, which makes agent scripts expressive and well understandable. They can be realized as (constraint) logic programs. The logical description language is ab ..."
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Cited by 15 (9 self)
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In this paper, we present a multilayered architecture for spatial and temporal agents. The focus is laid on the declarativity of the approach, which makes agent scripts expressive and well understandable. They can be realized as (constraint) logic programs. The logical description language is able to express actions or plans for one and more autonomous and cooperating agents for the RoboCup (Simulator League). The system architecture hosts constraint technology for qualitative spatial reasoning, but quantitative data is taken into account, too. The basic (hardware) layer processes the agent's sensor information. An interface transfers this lowlevel data into a logical representation. It provides facilities to access the preprocessed data and supplies several basic skills. The second layer performs (qualitative) spatial reasoning. On top of this, the third layer enables more complex skills such as passing, offsidedetection etc. At last, the fourth layer establishes acting as a team both by emergent and explicit cooperation. Logic and deduction provide a clean means to specify and also to implement teamwork behavior.
Elimination of equality via transformation with ordering constraints
 Lecture Notes in Computer Science
, 1421
"... Abstract. We refine Brand’s method for eliminating equality axioms by (i) imposing ordering constraints on auxiliary variables introduced during the transformation process and (ii) avoiding certain transformations of positive equations with a variable on one side. The refinements are both of theoret ..."
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Cited by 11 (1 self)
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Abstract. We refine Brand’s method for eliminating equality axioms by (i) imposing ordering constraints on auxiliary variables introduced during the transformation process and (ii) avoiding certain transformations of positive equations with a variable on one side. The refinements are both of theoretical and practical interest. For instance, the second refinement is implemented in Setheo and appears to be critical for that prover’s performance on equational problems. The correctness of this variant of Brand’s method was an open problem that is solved by the more general results in the present paper. The experimental results we obtained from a prototype implementation of our proposed method also show some dramatic improvements of the proof search in model elimination theorem proving. We prove the correctness of our refinements of Brand’s method by establishing a suitable connection to basic paramodulation calculi and thereby shed new light on the connection between different approaches to equational theorem proving. 1
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent
Model Elimination, Logic Programming and Computing Answers
 University of Koblenz
, 1995
"... We demonstrate that theorem provers using model elimination (ME) can be used as answer complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this, we develop a new calculus called ancestr ..."
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Cited by 10 (5 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answer complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this, we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers.
Computing Answers with Model Elimination
, 1997
"... We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry ..."
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Cited by 9 (2 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers. Keywords. Automated reasoning; theorem proving; model elimination; logic programming; computing answers. In first order automatic theorem proving one is interested in the question whether a given formula follows logically from a set of axioms. This is a rather artificial t...