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 ...

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...

N.B.: For the references, please see Selected Bibliography on Aristotle's Theory of Categorical Syllogism "When modem logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle’s contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotl...

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 ...

Apparently Ex Falso Quodlibet (or Explosion) cannot be isolated within CL (Classical Logic); if Explosion has to go, then so have other inference rules, for example either Addition or Disjunctive Syllogism. This certainly holds according to the standard abstract view on logic. However, as I shall show, it does not hold if a logic is defined by a procedure—a set of instructions to obtain a proof...

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such 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...

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...

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...