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There is an established equivalence between relatio nal database Functional Dependencies (FDs) and a fragment of switching algebra that is built typical ly of Horn clauses. This equivalence pertains to bo th concepts and procedures of the FD relational databa se domain and the switching algebraic domain. This study is an exposition of the use of switching -algebraic tools in solving problems typically encountered in the analysis and design of relationa l databases. The switching-algebraic tools utilized include purely-algebraic techniques, purely-visual techniques employing the Karnaugh map and intermediary techniques employing the variable-ente red Karnaugh map. The problems handled include; (a) the derivation of the closure of a Dep endency Set (DS), (b) the derivation of the closure of a set of attributes, (c) the determination of all c andidate keys and (d) the derivation of irredundant dependency sets equivalent to a given DS and conseq uently the determination of the minimal cover of such a set. A relatively large example illustrates the switching-algebraic approach and demonstrates i ts pedagogical and computational merits over the tradi tional approach.

In traditional propositional logic, many replacement and inference rules were involved to ascertain if the truth of several antecedents implied the truth of a particular consequent. This research described a powerful technique called the Modern Syllogistic Method (MSM), which ferreted out from a set of premises all that can be concluded from it and casted the resulting conclusions in the simplest and most compact form. We observed that all replacement rules were explicitly and inherently integrated within the MSM and proved that all inference rules were simply limited special cases of it. This meant that the MSM constituted a complete method of logic deduction. We also showed how to use the MSM in determining whether inconsistencies existed within a given set of premises and also in detecting formal logical fallacies. We demonstrated the applicability of the method in diverse fields via four examples that illustrated its mathematical details and exhibited the nature of conclusions it can come up with. In fact, these examples demonstrated the possibility of extracting deductions that were not so obvious and even surprising. The examples also showed how logic can be misused and how logic misuse can be avoided or detected.