Abstract
This chapter describes implementation of abductive and modified conclusions by means of NTA. The algorithm and rules to form hypotheses for abductive conclusions are proposed. They can be applied not only to NTA objects expressing formulas of propositional calculus, but also to a more general case when attribute domains contain more than two values. Within a specific knowledge system, choosing variables and their values depends on criteria determined by the content of the system. The techniques that we developed simplify generating abductive conclusions for given limitations, for instance, in composition and number of variables. A distinctive feature of the proposed methods is that they are based on the classical foundations of logic, that is, they do not use non-monotonic logic, the logic of defaults, etc., which allowed some violations of laws of Boolean algebra and algebra of sets.
Soon, people will improve their language to the extent sufficient to prove mathematically that two plus two equals seven. – Anton P. Chekhov
TopCollisions In Nta
Defeasible reasoning belongs to logical systems that admit changes of initial premises during inference. This results from the conjectural nature of some parts of knowledge used in such systems: the knowledge may need extending and improving. The said improvement is not always unambiguous; a suitable hypothesis has to be chosen from a variety of options. That is why we should define some specific correctness criteria for new knowledge.
When we consider reasoning where the incorrectness analysis is important (for instance, a search for discrepancies between some obtained results and facts or generally accepted statements), it turns out that incorrectness in modern classical logic is governed only by formal contradiction when premises lead to both a conclusion and its negation. This restriction is too strong: many situations that are seen as a contradiction or a paradox in everyday practice are not formal contradictions.