Automated deduction in paraconsistent logics

Annotated logics is a class of Paraconsistent logics that has been used to provide the semantical foundations of various reasoning systems that may contain useful inconsistent, or imprecise information. In this thesis, we investigate deduction techniques for Annotated logics. These techniques will serve as the bases for implementing the clausal subset of the logics. We first introduce a basic resolution proof procedure, called p-resolution, for performing deductions over clausal annotated logics. P-resolution contains two inference rules: Mega-resolution and Cloning. A number of experiments are conducted to analyze the efficiency of two variants of p-resolution. Secondly, we show that Annotated Logics is an instance of a more general class of Signed Logics. A comparison is made between p-resolution and the resolution procedure for signed logics, called signed resolution. This comparison reveals an interesting relationship between Mega-resolution and Cloning. We also study the efficiency of p-resolution as compared to signed resolution. Thirdly, we examine an extension to annotated logics that enables parallel representations of annotated clauses. This extension facilitates a generalization of p-resolution, called gp-resolution, that embeds parallel searching within the inference rule. It is shown that the generalized proof procedure is sound and complete. Lastly, we investigate some philosophical and practical issues relating to paraconsistent deductive databases. We analyze the intuitive meaning behind the closed world assumption when dealing with potentially inconsistent data. Using gp-resolution, we also introduce a query answering procedure for paraconsistent deductive databases that is similar to SLD-resolution for ordinary deductive databases.