Subjects completed a belief questionnaire that contained propositions of the form "X implies Y." In some cases, the questionnaire items included both premises and the conclusion of a syllogism of the form "A implies B, B implies C, A implies C" (e.g., "Taking vitamin C will increase resistance to infection," "Increasing resistance to infection will prevent colds," and "Taking vitamin C will pre...

This paper offers a logical formalisation of an argument-based account of reasoning about action, taking seriously the abductive nature of this form of reasoning. The particular question addressed is what is the best way to achieve a specified goal? Given a set of final goals and a set of rules on the effects of actions, the formation of subgoals for a goal is formalised as the application of a...

What is mathematical logic? Mathematical logic is the application of mathematical techniques to logic. What is logic? I believe I am following the ancient Greek philosopher Aristotle when I say that logic is the (correct) rearranging of facts to find the information that we want. Logic has two aspects: formal and informal. In a sense logic belongs to everyone although we often accuse others of ...

Abstract This paper gives an account of Anderson and Belnap’s selection criteria for adequate theory entailment. The are grouped into three categories: pertaining to modality, those relevance, related expressive strength. leitmotif both this its prequel is the relevant legitimacy disjunctive syllogism. Relevant logics commonly held be paraconsistent logics. It shown in paper, however, that E R ...

Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refuta...

Charles S. Peirce argued that, besides deduction and induction, there is a third mode of inference which he called "hypothesis" or "abduction". He characterized abduction as reasoning "from effect to cause", and as "the operation of adopting an explanatory hypothesis". Peirce's ideas about abduction, which are related also to historically earlier accounts of heuristic reasoning (the method of a...

In 1860, Augustus de Morgan published DeM60], thereby launching an investigation into the algebra of relations. This developed into the subject now called Algebraic Logic, though in the 19th century it was simply thought of as mathematical logic. This work, along with Frege's quantiier logic, became the foundation of modern logic and model theory. In De Morgan's writing there is no sharp separa...

ions are not at all that different from the personifications of the fairy tale" (p. 75). Statements about crazy behavior that ascribe agency to intrapsychic entities such as "impulses" or "internal pressures" are homologous to statements that the insane are ruled by demons. The anthropomorphisms of the former mode of explanation are more subtle and use terms that sound mechanical and impersonal...

This paper is a continuation of the formal theory of intermediate quantifiers (expressions such as most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of ) introduced by Novák in [12]. The theory is a fuzzy-logic formalization of the concept introduced by Peterson in his book [17]. In this paper, we syntactically prove that 105 generalized Aristotle’s syllogism...