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Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting. Such integrations are essential for supporting program development in dependently typed languages. We integrate the equational theorem prover Waldmeister and test it on more than 800 proof goals from the TPTP library. In contrast to previous approaches, the reconstruction of Waldmeister proofs within Mella is quite robust and does not generate a significant overhead to proof search. Mella thus yields a template for integrating more expressive theorem provers in more sophisticated languages.

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting. Such integrations are essential for supporting program development in dependently typed languages. We integrate the equational theorem prover Waldmeister and test it on more than 800 proof goals from the TPTP library. In contrast to previous approaches, the reconstruction of Waldmeister proofs within Mella is quite robust and does not generate a significant overhead to proof search. Mella thus yields a template for integrating more expressive theorem provers in more sophisticated languages.

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting. Such integrations are essential for supporting program development in dependently typed languages. We integrate the equational theorem prover Waldmeister and test it on more than 800 proof goals from the TPTP library. In contrast to previous approaches, the reconstruction of Waldmeister proofs within Mella is quite robust and does not generate a significant overhead to proof search. Mella thus yields a template for integrating more expressive theorem provers in more sophisticated languages.

The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal ''cloning'' of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.

The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal ''cloning'' of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.

Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.

This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using message-passing algorithms. The communication language between agents is restricted in such a manner that each agent can only communicate to its neighboring agent(s) by means of their common language. In this paper we provide a refutation-complete report procedure for automated theorem proving in order-sorted first-order logic in a subclass of distributed agent-based networks. Rather than studying and evaluating the performance improvement of the automated theorem proving in order-sorted first-order logic using parallel or distributed agents, this paper focuses on building proofs in order-sorted first-order logic in a distributed manner under the restriction that agents may report their knowledge or observations only with their predefined language.

This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using message-passing algorithms. The communication language between agents is restricted in such a manner that each agent can only communicate to its neighboring agent(s) by means of their common language. In this paper we provide a refutation-complete report procedure for automated theorem proving in order-sorted first-order logic in a subclass of distributed agent-based networks. Rather than studying and evaluating the performance improvement of the automated theorem proving in order-sorted first-order logic using parallel or distributed agents, this paper focuses on building proofs in order-sorted first-order logic in a distributed manner under the restriction that agents may report their knowledge or observations only with their predefined language.

The schematic CERES method [8] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction rule to the LK-calculus. In this work, we formalize a schematic version of the infinitary pigeonhole principle, which we call the Non-injectivity Assertion schema (NiA-schema), in the LKS-calculus [8], and analyse the clause set schema extracted from the NiA-schema using some of the structure provided by the schematic CERES method. To the best of our knowledge, this is the first appli- cation of the constructs built for proof analysis of proof schemata to a mathematical argument since its publication. We discuss the role of Automated Theorem Proving (ATP) in schematic proof analysis, as well as the shortcomings of the schematic CERES method concerning the formalization of the NiA-schema, namely, the expressive power of the schematic resolution calculus. We conclude with a discussion concerning the usage of ATP in schematic proof analysis.

The schematic CERES method [8] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction rule to the LK-calculus. In this work, we formalize a schematic version of the infinitary pigeonhole principle, which we call the Non-injectivity Assertion schema (NiA-schema), in the LKS-calculus [8], and analyse the clause set schema extracted from the NiA-schema using some of the structure provided by the schematic CERES method. To the best of our knowledge, this is the first appli- cation of the constructs built for proof analysis of proof schemata to a mathematical argument since its publication. We discuss the role of Automated Theorem Proving (ATP) in schematic proof analysis, as well as the shortcomings of the schematic CERES method concerning the formalization of the NiA-schema, namely, the expressive power of the schematic resolution calculus. We conclude with a discussion concerning the usage of ATP in schematic proof analysis.

The schematic CERES method [8] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction rule to the LK-calculus. In this work, we formalize a schematic version of the infinitary pigeonhole principle, which we call the Non-injectivity Assertion schema (NiA-schema), in the LKS-calculus [8], and analyse the clause set schema extracted from the NiA-schema using some of the structure provided by the schematic CERES method. To the best of our knowledge, this is the first appli- cation of the constructs built for proof analysis of proof schemata to a mathematical argument since its publication. We discuss the role of Automated Theorem Proving (ATP) in schematic proof analysis, as well as the shortcomings of the schematic CERES method concerning the formalization of the NiA-schema, namely, the expressive power of the schematic resolution calculus. We conclude with a discussion concerning the usage of ATP in schematic proof analysis.

Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of a set of given premises, using a set of fundamental postulates and following the method of logical inference. In this paper, we propose GraATP, a generalized framework for automated theorem proving in plane geometry. Our proposed method translates the geometric entities into nodes of a graph and the relations between them as edges of that graph. The automated system searches for different ways to reach the conclusion for a claim via graph traversal by which the validity of the geometric theorem is examined.

Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of a set of given premises, using a set of fundamental postulates and following the method of logical inference. In this paper, we propose GraATP, a generalized framework for automated theorem proving in plane geometry. Our proposed method translates the geometric entities into nodes of a graph and the relations between them as edges of that graph. The automated system searches for different ways to reach the conclusion for a claim via graph traversal by which the validity of the geometric theorem is examined.

OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language. Consistency and entailment checking are known to be undecidable for OWL 2 Full. We have translated a large fragment of the OWL 2 Full semantics into first-order logic, and used automated theorem proving systems to do reasoning based on this theory. The results are promising, and indicate that this approach can be applied in practice for effective OWL reasoning, beyond the capabilities of current Semantic Web reasoners. This is an extended version of a paper with the same title that has been published at CADE 2011, LNAI 6803, pp. 446-460. The extended version provides appendices with additional resources that were used in the reported evaluation.

The primary objective of this project is to develop a new model of natural human reasoning with imprecise linguistic information. Key to this model is a collection of abstraction mechanisms based on the concept of a linguistic variable, which was first introduced for this purpose within the context of a semantics based on fuzzy sets. The present approach differs from the earlier one, however, in that (1) it does not require the use of fuzzy sets for the interpretation of linguistic terms, and (2) the meanings of logical inferences are given as algorithms which act directly on terms themselves, rather than on their underlying interpretations. Thus this work constitutes a return to the more purely symbolic or aziomatic representations of logical deduction, whereas the fuzzy-sets model concerns denotational or semantic representations. The new model should not be viewed as a negation of the earlier approaches, however, but as an augmentation of them. The present work is intended as the beginning of a larger system which encompasses both styles of reasoning. Also underway is development of a prototype expert system shell which implements the new model, together with some of the earlier forms of fuzzy inference. This part of the work is being undertaken in part to identify the problems associated with the task of implementation and in this manner demonstrate that implementation is indeed possible. Development of the prototype is also desired so as to experiment with the model and determine its viability as a basis for reasoning in specific problem domains.

Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.

While more and more data is stored and accessed electronically, better access control methods need to be implemented for computer security. Formal modelling and analysis have been successfully used in certain areas of computer systems, such as verifying the security properties of cryptographic and authentication protocols. However, formal models for computer systems in cyberspace, like networks, have hardly advanced. A highly regarded graduate textbook cites the Take-Grant model created in 1977 as one of the current examples of security modelling and analysis techniques. This model is rarely used in practice though. This research implements the Take-Grant Protection model's four de jure rules and Can Share predicate in the Prototype Verification System (PVS) which automates model checking and theorem proving. This facilitates the ability to test a given Take-Grant model against many systems which are modelled using digraphs. Two models, one with error checking and one without, are created to implement take-grant rules. The first model that does not have error checking incorporated requires manual error checking. The second model uses recursion to allow for the error checking. The Can Share theorem requires further development.

The amount and complexity of software developed during the last few years has increased tremendously. In particular, programs are being used more and more in embedded systems (from car-brakes to plant-control). Many of these applications are safety-relevant, i.e. a malfunction of hardware or software can cause severe damage or loss. Tremendous risks are typically present in the area of aviation, (nuclear) power plants or (chemical) plant control. Here, even small problems can lead to thousands of casualties and huge financial losses. Large financial risks also exist when computer systems are used in the area of telecommunication (telephone, electronic commerce) or space exploration. Computer applications in this area are not only subject to safety considerations, but also security issues are important. All these systems must be designed and developed to guarantee high quality with respect to safety and security. Even in an industrial setting which is (or at least should be) aware of the high requirements in Software Engineering, many incidents occur. For example, the Warshaw Airbus crash, was caused by an incomplete requirements specification. Uncontrolled reuse of an Ariane 4 software module was the reason for the Ariane 5 disaster. Some recent incidents in the telecommunication area, like illegal "cloning" of smart-cards of D2GSM handies, or the extraction of (secret) passwords from German T-online users show that also in this area serious flaws can happen. Due to the inherent complexity of computer systems, most authors claim that only a rigorous application of formal methods in all stages of the software life cycle can ensure high quality of the software and lead to real safe and secure systems. In this paper, we will have a look, in how far automated theorem proving can contribute to a more widespread application of formal methods and their tools, and what automated theorem provers (ATPs) must provide in order to be useful.