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Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) |
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This is the second part of the paper [Part I] which appeared in the previous issue of this journal. |
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Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local (...) |
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In this paper I use the distinction between hard and soft information from the dynamic epistemic logic tradition to extend prior work on informational conceptions of logic to include non-monotonic consequence-relations. In particular, I defend the claim that at least some non-monotonic logics can be understood on the basis of soft or “belief-like” logical information, and thereby question the orthodox view that all logical information is hard, “knowledge-like”, information. |
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The aim of this paper is to argue that logic can play an important role in the “toolbox” of molecular biology. We show how biochemical pathways, i.e., transitions from a molecular aggregate to another molecular aggregate, can be viewed as deductive processes. In particular, our logical approach to molecular biology — developed in the form of a natural deduction system — is centered on the notion of Curry-Howard isomorphism, a cornerstone in nineteenth-century proof-theory. |
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The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) |
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Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) |
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This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. (...) |
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ABSTRACT The two main directions pursued in the present paper are the following. The first direction was started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than (...) |
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Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...) |
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Where is logic heading today? There is a general feeling that the discipline is broadening its scope and agenda beyond classical foundational issues, and maybe even a concern that, like Stephen Leacock’s famous horseman, it is ‘riding off madly in all directions’. So, what is the resultant vector? There seem to be two broad answers in circulation today. One is logical pluralism, locating the new scope of logic in charting a wide variety of reasoning styles, often marked by non-classical structural (...) |
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This paper deals with the problem of universality property of logic. At first, this property is analyzed in the context of first-order logic. Three senses of the universality property are distinguished: universal applicability, topical neutrality and validity. All theses senses can be proved to be justified. The fourth understanding, namely the amount of expressive power, is connected with the criticism of the first-order thesis: first-order logic is the logic. The categorical approach to logic is presented as associated with the last (...) |
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This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh'' and, more generally, evidence confirming each ofh1, h2, ..., hm confirms at least one of h1, h2,ldots;, hn''.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classical logics developed in the twentieth century. Oneaspect (...) |
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