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Journals and Conferences
The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.
It is a task of philosophical logic to investigate the concepts central to our reasoning. This is a matter of conceptual analysis, distinguished by the fact that the concepts analyzed are basic ones, occurring in reasoning about a wide range of topics. Since reasoning is generally expressible in speech or writing (this seems a necessary truth, though some… (More)
Here is a familiar history: modal logics (see ) were around for some time before a semantic framework was found for them (by Kripke and others).1 This framework did at least two Very Good Things for modal logics: 1) it connected the powerful mathematical tools of model theory to these logics, allowing a variety of technical results to be proven, and 2)… (More)
The representation of quantification over relations in monadic third-order logic is discussed; it is shown to be possible in numerous special cases of foundational interest, but not in general unless something akin to the Axiom of Choice is assumed.
After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell’s Principia Mathematica with the axiom of infinity but without the axiom of reducibility. 1 Historical introduction After discovering the inconsistency in Frege’s Grundgesetze der Arithmetik, Russell proposed two changes: first,… (More)
We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula φ in the propositional modal language with A, there is a formula ψ not containing A such that φ and ψ are materially equivalent at the actual world in… (More)