The KE inference system is a tableau method developed by Marco Mondadori which was presented as an improvement, in the computational efficiency sense, over Analytic Tableaux. In the literature, there is no description of a theorem prover based on the KE method for the C"1 paraconsistent logic. Paraconsistent logics have several applications, such as in robot control and medicine. These applications could benefit from the existence of such a prover. We present a sound and complete KE system for C"1, an informal specification of a strategy for the C"1 prover as well as problem families that can be used to evaluate provers for C"1. The C"1KE system and the strategy described in this paper will be used to implement a KE based prover for C"1, which will be useful for those who study and apply paraconsistent logics.
In @cite_19 , another tableau system (obtained via a uniform procedure) was presented. It is based on analytic tableaux and has too many branching rules.
@cite_19
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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 In this paper we present a new hierarchy of analytical tableaux systems TNDC"n,1@?n =1, as primitive operators, differently to what has been done in the literature, where these operators are usually defined operators. We prove a version of Cut Rule for the TNDC"n,1@?n<@w, and also prove that these systems are logically equivalent to the corresponding systems C"n,1@?n<@w. The systems TNDC"n constitute completely automated theorem proving systems for the systems of da Costa's hierarchy C"n,1@?n<@w. The paper presents a one-pass tableau calculus PLTLT for the propositional linear time logic PLTL. The calculus is correct and complete and unlike in previous decision methods, there is no second phase that checks for the fulfillment of the so-called eventuality formulae. This second phase is performed locally and is incorporated into the rules of the calculus. Derivations in PLTLT are cyclic trees rather than cyclic graphs. When used as a basis for a decision procedure, it has the advantage that only one branch needs to be kept in memory at any one time. It may thus be a suitable starting point for the development of a parallel decision method for PLTL. Classifying a set of objects into clusters can be done in numerous ways, producing different results. They can be visually compared using contingency tables [27], mosaicplots [13], fluctuation diagrams [15], tableplots [20] , (modified) parallel coordinates plots [28], Parallel Sets plots [18] or circos diagrams [19]. Unfortunately the interpretability of all these graphical displays decreases rapidly with the numbers of categories and clusterings. In his famous book A Semiology of Graphics [5] Bertin writes “the discovery of an ordered concept appears as the ultimate point in logical simplification since it permits reducing to a single instant the assimilation of series which previously required many instants of study”. Or in more everyday language, if you use good orderings you can see results immediately that with other orderings might take a lot of effort. This is also related to the idea of effect ordering [12], that data should be organised to reflect the effect you want to observe. This paper presents an efficient algorithm based on Bertin's idea and concepts related to Kendall's t [17], which finds informative joint orders for two or more nominal classification variables. We also show how these orderings improve the various displays and how groups of corresponding categories can be detected using a top-down partitioning algorithm. Different clusterings based on data on the environmental performance of cars sold in Germany are used for illustration. All presented methods are available in the R package extracat which is used to compute the optimized orderings for the example dataset.