Renate A. Schmidt

Automated Deduction - CADE-22

Session 1. Invited Talk.- Integrated Reasoning and Proof Choice Point Selection in the Jahob System - Mechanisms for Program Survival.- Session 2. Combinations and Extensions.- Superposition and Model Evolution Combined.- On Deciding Satisfiability by DPLL( ) and Unsound Theorem Proving.- Combinable Extensions of Abelian Groups.- Locality Results for Certain Extensions of Theories with Bridging Functions.- Session 3. Minimal Unsatisfiability and Automated Reasoning Support.- Axiom Pinpointing in Lightweight Description Logics via Horn-SAT Encoding and Conflict Analysis.- Does This Set of Clauses Overlap with at Least One MUS?.- Progress in the Development of Automated Theorem Proving for Higher-Order Logic.- Session 4. System Descriptions.- System Description: H-PILoT.- SPASS Version 3.5.- Dei: A Theorem Prover for Terms with Integer Exponents.- veriT: An Open, Trustable and Efficient SMT-Solver.- Divvy: An ATP Meta-system Based on Axiom Relevance Ordering.- Session 5. Invited Talk.- Instantiation-Based Automated Reasoning: From Theory to Practice.- Session 6. Interpolation and Predicate Abstraction.- Interpolant Generation for UTVPI.- Ground Interpolation for Combined Theories.- Interpolation and Symbol Elimination.- Complexity and Algorithms for Monomial and Clausal Predicate Abstraction.- Session 7. Resolution-Based Systems for Non-classical Logics.- Efficient Intuitionistic Theorem Proving with the Polarized Inverse Method.- A Refined Resolution Calculus for CTL.- Fair Derivations in Monodic Temporal Reasoning.- Session 8. Termination Analysis and Constraint Solving.- A Term Rewriting Approach to the Automated Termination Analysis of Imperative Programs.- Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic.- Session 9. Invited Talk.- Building Theorem Provers.- Session 10. Rewriting, Termination and Productivity.- Termination Analysis by Dependency Pairs and Inductive Theorem Proving.- Beyond Dependency Graphs.- Computing Knowledge in Security Protocols under Convergent Equational Theories.- Complexity of Fractran and Productivity.- Session 11. Models.- Automated Inference of Finite Unsatisfiability.- Decidability Results for Saturation-Based Model Building.- Session 12. Modal Tableaux with Global Caching.- A Tableau Calculus for Regular Grammar Logics with Converse.- An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability.- Session 13. Arithmetic.- Volume Computation for Boolean Combination of Linear Arithmetic Constraints.- A Generalization of Semenovs Theorem to Automata over Real Numbers.- Real World Verification.

Resolution-Based Methods for Modal Logics

In this paper we give an overview of resolution methods for extended propositional modal logics. We adopt the standard translation approach and consider different resolution refinements which provide decision procedures for the resulting clause sets. Our procedures are based on ordered resolution and selection-based resolution. The logics that we cover are multi-modal logics defined over relations closed under intersection, union, converse and possibly complementation.

MSPASS: Modal Reasoning by Translation and First-Order Resolution

mspass is an extension of the first-order theorem prover spass, which can be used as a modal logic theorem prover, a theorem prover for description logics and a theorem prover for the relational calculus.

Issues of Decidability for Description Logics in the Framework of Resolution

We describe two methods on the basis of which efficient resolution decision procedures can be developed for a range of description logics. The first method uses an ordering restriction and applies to the description logic ALB, which extends ALC with the top role, full role negation, role intersection, role disjunction, role converse, domain restriction, range restriction, and role hierarchies. The second method is based solely on a selection restriction and applies to reducts of ALB without the top role and role negation. The latter method can be viewed as a polynomial simulation of familiar tableaux-based decision procedures. It can also be employed for automated model generation.

System Description: Spass Version 3.0

An electrophotographic copying system is disclosed wherein the DC charging and DC transfer corotrons are powered with an unfiltered full wave rectified voltage derived from a 110 volt, 60 hertz line source. The DC corotrons are regulated along with AC corotrons used for detack and erase operations. The regulation is achieved by a feedback loop coupled to only one of the corotrons.

An empirical analysis of modal theorem provers

ABSTRACT 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 KRZIS, the sequent-based Logics Workbench, and a translation approach combined with the first-order theorem prover SPASS. Our benchmark suites are sets of multi-modal formulae in a certain normal form randomly generated according to the scheme of Giunchiglia and Sebastiani [GS 96a, GS 96b]. We investigate the quality of the random modal formulae and show that the scheme has some shortcomings, which may lead to mistaken conclusions. We propose improvements to the evaluation method and show that the translation approach provides a viable alternative to the other approaches.

4 Computational modal logic

Publisher Summary This chapter examines computational approaches to modal logics. A variety of computational approaches and reasoning problems are considered, the use of translation-based and tableau-based algorithms for deciding the satisfiability of a formula is focused, both with and without reference to a background theory. The dominance of translation-based and tableau-based approaches in implemented systems, and by the importance of satisfiability testing in applications such as the verification of multi-agent systems and ontology engineering is examined. The reason for the dominance of these two approaches is that they have proved amenable to implementation and optimization techniques that dramatically improve typical case performance; the use of such techniques is crucial if reasoning systems are to be effective in applications. The applicability and effectiveness of optimization techniques and refinements is highly dependent on the logic under consideration and on the class of problem being solved. The choice of approach depend on the logic in question: tableau-based methods seem to have some advantages in the presence of graded modalities (counting), whereas translation-based methods can handle and may be better for Boolean modal logics.

Using Resolution for Testing Modal Satisfiability and Building Models

This paper presents a translation-based resolution decision procedure for the multimodal logic K(m)(∩,∪,⌣) defined over families of relations closed under intersection, union, and converse. The relations may satisfy certain additional frame properties. Different from previous resolution decision procedures that are based on ordering refinements, our procedure is based on a selection refinement, the derivations of which correspond to derivations of tableaux or sequent proof systems. This procedure has the advantage that it can be used both as a satisfiability checker and as a model builder. We show that tableaux and sequent-style proof systems can be polynomially simulated with our procedure. Furthermore, the finite model property follows for a number of extended modal logics.

A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae

In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity, Euclideanness and functionality, to decidable logics. The goal of the axiomatic translation principle is to find simplified theories, which capture the inference problems in the original theory, but in a way that is more amenable to automation and easier to deal with by existing theorem provers. The principle of the axiomatic translation is conceptually very simple and can be largely automated. Soundness is automatic under reasonable assumptions, and termination of ordered resolution is easily achieved, but the non-trivial part of the approach is proving completeness.

Using tableau to decide expressive description logics with role negation

This paper presents a tableau approach for deciding description logics outside the scope of OWL DL/1.1 and current state-of-the-art tableau-based description logic systems. In particular, we define a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics with full role negation. ALBO is the extension of ALC with the Boolean role operators, inverse of roles, domain and range restriction operators and it includes full support for nominals (individuals). ALBO is a very expressive description logic which subsumes Boolean modal logic and the two-variable fragment of first-order logic and reasoning in it is NExpTime-complete. An important novelty is the use of a generic, unrestricted blocking rule as a replacement for standard loop checking mechanisms implemented in description logic systems. An implementation of our approach exists in the METTEL system.