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We present a proof searching technique for the natural deduction calculus for the propositional linear-time temporal logic and prove its correctness. This opens the prospect to apply our technique as an automated reasoning tool in a number of emerging computer science applications and in a deliberative decision making framework across various AI applications.

Abstract. We present a natural deduction calculus for the propositional linear-time temporal logic and prove its correctness. The system extends the natural deduction construction of the classical propositional logic. This will open the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various AI applications.

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A temporal clausal resolution method was originally developed for linear time temporal logic and further extended to the branching-time framework of Computation Tree Logic (CTL). In this paper, following our general idea to expand the applicability of this efficient method to more expressive formalisms useful in a variety of applications in computer science and AI requiring branching time logics, we define a clausal resolution technique for Extended Computation Tree Logic (ECTL). The branching-time temporal logic ECTL is strictly more expressive than CTL in allowing fairness operators. The key elements of the resolution method for ECTL, namely the clausal normal form, the concepts of step resolution and a temporal resolution, are introduced and justified with respect to this new framework. Although in developing these components we incorporate many of the techniques defined for CTL, we need novel mechanisms in order to capture fairness together with the limit closure property of the underlying tree models. We accompany our presentation of the relevant techniques by examples of the application of the temporal resolution method. Finally, we provide a correctness argument and consider future work discussing an extension of the method yet further, to the logic CTL * , the most powerful logic of this class.

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In this paper, we propose a novel intelligent methodology to construct a Bankruptcy Prediction Computation Model, which is aimed to execute a company's financial status analysis accurately. Based on the semantic data analysis and management, our methodology considers Semantic Database System as the core of the system. It comprises three layers: an Ontology of Bankruptcy Prediction, Semantic Search Engine, and a Semantic Analysis Graph Database system.The Ontological layer defines the basic concepts of the financial risk management as well as the objects that serve as sources of knowledge for predicting a company's bankruptcy. The Graph Database layer utilises a powerful semantic data technology, which serves as a semantic data repository for our model.The article provides a detailed description of the construction of the Ontology and its informal conceptual representation. We also present a working prototype of the Graph Database system, constructed using the Neo4j application, and show the connection between well-known financial ratios.We argue that this methodology which utilises state of the art semantic data management mechanisms enables data processing and relevant computations in a more efficient way than approaches using the traditional relational database. These give us solid grounds to build a system that is capable of tackling the data of any complexity level.