• Formal verification techniques can, in theory, prove beyond a doubt that a system is implemented correctly. • In practice, there are still many challenges, but there are

Sledgehammer integrates third-party automatic theorem provers in the proof assistant Isa-belle/HOL. In the seven years since its first release in 2007, it has grown to become an essential part of most Isabelle users’ workflow. Although a lot of effort has gone into tuning the system, the main

mechanisms are applied on these ontologies, even minimal inconsistencies oftentimes lead to serious errors and are hard to trace back and find. This paper addresses this issue and describes a method to validate ontologies using an automatic theorem prover and MultiNet axioms. This logic-based approach allows

The concepts of implicates and implicants are widely used in several fields of "Automated Reasoning". Particularly, our research group has developed several techniques that allow us to reduce efficiently the size of the input, and therefore the complexity of the problem. These techniques are based on obtaining and using implicit information that is collected in terms of unitary implicates and implicants. Thus, we require efficient algorithms to calculate them. In classical propositional logic it is easy to obtain efficient algorithms to calculate the set of unitary implicants and implicates of a formula. In temporal logics, contrary to what we see in classical propositional logic, these sets may contain infinitely many members. Thus, in order to calculate them in an efficient way, we have to base the calculation on the theoretical study of how these sets behave. Such a study reveals the need to make a generalization of Lattice Theory, which is very important in "Computational Algebra". In this paper we introduce the multisemilattice structure as a generalization of the semilattice structure. Such a structure is proposed as a particular type of poset. Subsequently, we offer an equivalent algebraic characterization based on non-deterministic operators and with a weakly associative property. We also show that from the structure of multisemilattice we can obtain an algebraic characterization of the multilattice structure. This paper concludes by showing the relevance of the multisemilattice structure in the design of algorithms aimed at calculating unitary implicates and implicants in temporal logics. Concretely, we show that it is possible to design efficient algorithms to calculate the unitary implicants/implicates only if the unitary formulae set has the multisemilattice structure.

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Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for Meti-Tarski, an automatic theorem prover for real-valued special functions such as exp, ln, sin, cos and tan −1. The experimental findings confirm

Abstract. aRa is an automatic theorem prover for various kinds of relation algebras. It is based on Gordeev’s Reduction Predicate Calculi for n-variable logic (RPCn) which allow first-order finite variable proofs. Employing results from Tarski/Givant and Maddux we can prove validity in the theories

We describe work in progress on an automatic theorem prover for recursive function theory that we intend to apply in the analysis (including verification and transformation) of useful computer programs. The mathematical theory of our theorem prover is extendible by the user and serves as a logical

Abstract. LEO-II is a standalone, resolution-based higher-order theorem prover designed for effective cooperation with specialist provers for natural fragments of higher-order logic. At present LEO-II can cooperate with the first-order automated theorem provers E, SPASS, and Vampire. The improved

Abstract Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which