A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.     

A logical calculus with descriptions

Journal of Philosophical Logic -     

A plea for logical objects

An account of validity that makes what is invalid conditional on how many individuals there are is what I call a conditional account of validity. Here I defend conditional accounts against a criticism derived from Etchemendy’s well-known criticism of the model-theoretic analysis of validity. The criticism is essentially that knowledge of the size of the universe is non-logical and so by making knowledge of the extension of validity depend on knowledge of how many individuals there are, conditional accounts fail to reflect that the former knowledge is basic, i.e., independent of knowledge derived from other sciences. Appealing to Russell’s pre-Principia logic, I defend conditional accounts against this criticism by sketching a rationale for thinking that there are infinitely many logical objects.     

A defense of contingent logical truths

A formula is a contingent logical truth when it is true in every model M but, for some model M, false at some world of M. We argue that there are such truths, given the logic of actuality. Our argument turns on defending Tarski’s definition of truth and logical truth, extended so as to apply to modal languages with an actuality operator. We argue that this extension is the philosophically proper account of validity. We counter recent arguments to the contrary presented in Hanson’s ‘Actuality, Necessity, and Logical Truth’ (Philos Stud 130:437–459, 2006).     

A dialogical route to logical pluralism

This paper argues that adopting a particular dialogical account of logical consequence quite directly gives rise to an interesting form of logical pluralism, the form of pluralism in question arising out of the requirement that deductive proofs be explanatory.

     

A geometric interpretation of logical formulae

Summary The aim of this paper is to give a geometric interpretation of quantifiers in the intutionistic predicate calculus. We obtain it treating formulae withn free variables as functions withn arguments which run over an abstract set whereas the values of functions are open subsets of a suitable topological space.     

A logical calculus for controlled monotonicity

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes.     

A possible extension of logical theory?

Philosophical Studies -