206 research outputs found
Saturation-based decision procedures for extensions of the guarded fragment
We apply the framework of Bachmair and Ganzinger for saturation-based theorem proving to derive a range of decision procedures for logical formalisms, starting with a simple terminological language EL, which allows for conjunction and existential restrictions only, and ending with extensions of the guarded fragment with equality, constants, functionality, number restrictions and compositional axioms of form S ◦ T ⊆ H. Our procedures are derived in a uniform way using standard saturation-based calculi enhanced with simplification rules based on the general notion of redundancy. We argue that such decision procedures can be applied for reasoning in expressive description logics, where they have certain advantages over traditionally used tableau procedures, such as optimal worst-case complexity and direct correctness proofs.Wir wenden das Framework von Bachmair und Ganzinger fĂŒr saturierungsbasiertes Theorembeweisen an, um eine Reihe von Entscheidungsverfahren fĂŒr logische Formalismen abzuleiten, angefangen von einer simplen terminologischen Sprache EL, die nur Konjunktionen und existentielle Restriktionen erlaubt, bis zu Erweiterungen des Guarded Fragment mit Gleichheit, Konstanten, FunktionalitĂ€t, Zahlenrestriktionen und Kompositionsaxiomen der Form S ◦ T ⊆ H. Unsere Verfahren sind einheitlich abgeleitet unter Benutzung herkömmlicher saturierungsbasierter KalkĂŒle, verbessert durch Simplifikationsregeln, die auf dem Konzept der Redundanz basieren. Wir argumentieren, daĂ solche Entscheidungsprozeduren fĂŒr das Beweisen in ausdrucksvollen Beschreibungslogiken angewendet werden können, wo sie gewisse Vorteile gegenĂŒber traditionell benutzten Tableauverfahren besitzen, wie z.B. optimale worst-case KomplexitĂ€t und direkte Korrektheitsbeweise
Identification of Design Principles
This report identifies those design principles for a (possibly new) query and transformation
language for the Web supporting inference that are considered essential. Based upon these
design principles an initial strawman is selected. Scenarios for querying the Semantic Web
illustrate the design principles and their reflection in the initial strawman, i.e., a first draft of
the query language to be designed and implemented by the REWERSE working group I4
A theory of resolution
We review the fundamental resolution-based methods for first-order theorem proving and present them in a uniform framework. We show that these calculi can be viewed as specializations of non-clausal resolution with simplification. Simplification techniques are justified with the help of a rather general notion of redundancy for inferences. As simplification and other techniques for the elimination of redundancy are indispensable for an acceptable behaviour of any practical theorem prover this work is the first uniform treatment of resolution-like techniques in which the avoidance of redundant computations attains the attention it deserves. In many cases our presentation of a resolution method will indicate new ways of how to improve the method over what was known previously. We also give answers to several open problems in the area
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Automated verification of refinement laws
Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs
Discovering, quantifying, and displaying attacks
In the design of software and cyber-physical systems, security is often
perceived as a qualitative need, but can only be attained quantitatively.
Especially when distributed components are involved, it is hard to predict and
confront all possible attacks. A main challenge in the development of complex
systems is therefore to discover attacks, quantify them to comprehend their
likelihood, and communicate them to non-experts for facilitating the decision
process. To address this three-sided challenge we propose a protection analysis
over the Quality Calculus that (i) computes all the sets of data required by an
attacker to reach a given location in a system, (ii) determines the cheapest
set of such attacks for a given notion of cost, and (iii) derives an attack
tree that displays the attacks graphically. The protection analysis is first
developed in a qualitative setting, and then extended to quantitative settings
following an approach applicable to a great many contexts. The quantitative
formulation is implemented as an optimisation problem encoded into
Satisfiability Modulo Theories, allowing us to deal with complex cost
structures. The usefulness of the framework is demonstrated on a national-scale
authentication system, studied through a Java implementation of the framework.Comment: LMCS SPECIAL ISSUE FORTE 201
Scaling Up Description Logic Reasoning by Distributed Resolution
Benefits from structured knowledge representation have motivated the creation of large description logic ontologies. For accessing implicit information and avoiding errors in ontologies, reasoning services are necessary. However, the available reasoning methods suffer from scalability problems as the size of ontologies keeps growing.
This thesis investigates a distributed reasoning method that improves scalability by splitting a reasoning process into a set of largely independent subprocesses. In contrast to most description logic reasoners, the proposed approach is based on resolution calculi. We prove that the method is sound and complete for first order logic and different description logic subsets. Evaluation of the implementation shows a heavy decrease of runtime compared to reasoning on a single machine. Hence, the increased computation power pays off the overhead caused by distribution. Dependencies between subprocesses can be kept low enough to allow efficient distribution.
Furthermore, we investigate and compare different algorithms for computing the distribution of axioms and provide an optimization of the distributed reasoning method that improves workload balance in a dynamic setting
Efficient reasoning procedures for complex first-order theories
The complexity of a set of first-order formulas results from the size of the set and the complexity of the problem described by its formulas.
Decision Procedures for Ontologies
This thesis presents new superposition based decision procedures for large sets of formulas. The sets of formulas may contain expressive constructs like transitivity and equality. The procedures decide the consistency of knowledge bases, called ontologies, that consist of several million formulas and answer complex queries with respect to these ontologies. They are the first superposition based reasoning procedures for ontologies that are at the same time efficient, sound, and complete. The procedures are evaluated using the well-known ontologies YAGO, SUMO and CYC. The results of the experiments, which are presented in this thesis, show that these procedures decide the consistency of all three above-mentioned ontologies and usually answer queries within a few seconds.
Reductions for General Automated Theorem Proving
Sophisticated reductions are important in order to obtain efficient reasoning procedures for complex, particularly undecidable problems because they restrict the search space of theorem proving procedures. In this thesis, I have developed a new powerful reduction rule. This rule enables superposition based reasoning procedures to find proofs in sets of complex formulas. In addition, it increases the number of problems for which superposition is a decision procedure.Die KomplexitĂ€t einer Formelmenge fĂŒr einen automatischen Theorembeweiser in PrĂ€dikatenlogik 1. Stufe ergibt sich aus der Anzahl der zu betrachtenden Formeln und aus der KomplexitĂ€t des durch die Formeln beschriebenen Problems.
Entscheidungsprozeduren fĂŒr Ontologien
Diese Arbeit entwickelt effiziente auf Superposition basierende Beweisprozeduren fĂŒr sehr groĂe entscheidbare Formelmengen, die ausdrucksstarke Konstrukte, wie TransitivitĂ€t und Gleichheit, enthalten. Die Prozeduren ermöglichen es Wissenssammlungen, sogenannte Ontologien, die aus mehreren Millionen Formeln bestehen, auf Konsistenz hin zu ĂŒberprĂŒfen und Antworten auf komplizierte Anfragen zu berechnen. Diese Prozeduren sind die ersten auf Superposition basierten Beweisprozeduren fĂŒr groĂe, ausdrucksstarke Ontologien, die sowohl korrekt und vollstĂ€ndig, als auch effizient sind.
Die entwickelten Prozeduren werden anhand der weit bekannten Ontologien YAGO, SUMO und CYC evaluiert. Die Experimente zeigen, dass diese Prozeduren die Konsistenz aller untersuchten Ontologien entscheiden und Anfragen in wenigen Sekunden beantworten.
Reduktionen fĂŒr allgemeines Theorembeweisen
Um effiziente Prozeduren fĂŒr das Beweisen in sehr schwierigen und insbesondere in unentscheidbaren Formelmengen zu erhalten, sind starke Reduktionsregeln, die den Beweisraum einschrĂ€nken, von essentieller Bedeutung. Diese Arbeit entwickelt eine neue mĂ€chtige Reduktionsregel, die es Superposition ermöglicht Beweise in sehr schwierigen Formelmengen zu finden und erweitert die Menge von Problemen, fĂŒr die Superposition eine Entscheidungsprozedur ist
Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints
The monadic shallow linear Horn fragment is well-known to be decidable and
has many application, e.g., in security protocol analysis, tree automata, or
abstraction refinement. It was a long standing open problem how to extend the
fragment to the non-Horn case, preserving decidability, that would, e.g.,
enable to express non-determinism in protocols. We prove decidability of the
non-Horn monadic shallow linear fragment via ordered resolution further
extended with dismatching constraints and discuss some applications of the new
decidable fragment.Comment: 29 pages, long version of CADE-26 pape
Consequence Based Procedure for Description Logics with Self Restriction
We present a consequence based classification procedure for the description logics with self restriction constructor. Due to the difficulty of constructing a concept inclusion model for self restriction, we use a different proof by showing that all the completion rules can simulate all the corresponding ordered resolution inferences
Handling Transitive Relations in First-Order Automated Reasoning
We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations
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