This paper describes a resolution based Description Logic reasoning system called DLog. DLog transforms Description Logic axioms into a Prolog program and uses the standard Prolog execution for efficiently answering instance retrieval queries. From the Description Logic point of view, DLog is an ABox reasoning engine for the full SHIQ language. The DLog approach makes it possible to store the individuals in a database instead of memory, which results in better scalability and helps using description logic ontologies directly on top of existing information sources. To appear in Theory and Practice of Logic Programming (TPLP).
@cite_10 discuss how a first-order theorem prover, such as Vampire, can be modified and optimised for reasoning over description logic knowledge bases. This work, however, mostly focuses on TBox reasoning.
@cite_10
1807555267 1781094 2221495694 1819951499
In this article we describe VAMPIRE: a high-performance theorem prover for first-order logic. As our description is mostly targeted to the developers of such systems and specialists in automated reasoning, it focuses on the design of the system and some key implementation features. We also analyze the performance of the prover at CASC-JC. In this paper we give a short introduction in first-order theorem proving and the use of the theorem prover Vampire. We discuss the superposition calculus and explain the key concepts of saturation and redundancy elimination, present saturation algorithms and preprocessing, and demonstrate how these concepts are implemented in Vampire. Further, we also cover more recent topics and features of Vampire designed for advanced applications, including satisfiability checking, theory reasoning, interpolation, consequence elimination, and program analysis. This paper describes a new architecture for first-order resolution and superposition theorem provers called AVATAR (Advanced Vampire Architecture for Theories and Resolution). Its original motivation comes from a problem well-studied in the past  dealing with problems having clauses containing propositional variables and other clauses that can be split into components with disjoint sets of variables. Such clauses are common for problems coming from applications, for example in program verification and program analysis, where many ground literals occur in the problems and even more are generated during the proof-search. This problem was previously studied by adding various versions of splitting. The addition of splitting resulted in some improvements in performance of theorem provers. However, even with various versions of splitting, the performance of superposition theorem provers is nowhere near SMT solvers on variable-free problems or SAT solvers on propositional problems. This paper describes a new architecture for superposition theorem provers, where a superposition theorem prover is tightly integrated with a SAT or an SMT solver. Its implementation in our theorem prover Vampire resulted in drastic improvements over all previous implementations of splitting. Over four hundred TPTP problems previously unsolvable by any modern prover, including Vampire itself, have been proved, most of them with short runtimes. Nearly all problems solved with one of 481 variants of splitting previously implemented in Vampire can also be solved with AVATAR. We also believe that AVATAR is an important step towards efficient reasoning with both quantifiers and theories, which is one of the key areas in modern applications of theorem provers in program analysis and verification. A generic tableau prover has been implemented and integrated with Isabelle (Paulson, 1994). Compared with classical first-order logic provers, it has numerous extensions that allow it to reason with any supplied set of tableau rules. It has a higherorder syntax in order to support user-defined binding operators, such as those of set theory. The unification algorithm is first-order instead of higher-order, but it includes modifications to handle bound variables. The proof, when found, is returned to Isabelle as a list of tactics. Because Isabelle verifies the proof, the prover can cut corners for efficiency’s sake without compromising soundness. For example, the prover can use type information to guide the search without storing type information in full. Categories: F.4, I.1