Rejection in Łukasiewicz's and Słupecki's Sense

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic

Who is Telling the Truth…… Cognitive Processes in Meta-Deductive Reasoning

How can the mechanisms underlying both human and computer reasoning develop to deal with novel or complex inferences ? The answer may lie in research in the cognitive science of me ta-deductions. Some meta-deductions, such as the inferences we make when we try to think about what other people are thinking, are central to successful social and professional interactions, and to the interactions of people with computers. Other meta-deductions, such as the inferences we make when we try to work out the truth or falsity of alternative states of affairs, can seem both novel and complex. Consider, for example, an island inhabited by two sorts of people, knights who always tell the truth, and knaves who always lie. Suppose you overhear a conversation between two of these individuals. A asserts, I am a knight and B is a knight. B asserts, A is a knave. Can you work out whether A is a knight or a knave, and whether B is a knight or a knave? In this chapter, we examine experimental data on the sorts of inferences that human reasoners make from these puzzles. The data help us to chose from among the programs developed to simulate theories of the mechanisms underlying these inferences.13 page(s