This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...) presenting some interesting open problems. It will be of interest to a range of readers including advanced students of logic, philosophical and mathematical logicians, and computer scientists. (shrink)

The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A V (...) B) -> (A V for all xB). with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation. (shrink)

Models are constructed for a variety of systems of quantified relevance logic with identity. Models are given for systems with different principles governing the transitivity of identity and substitution, and the relative merits of these principles are discussed. The models in this paper are all extensions of the semantics of Fine's Semantics for Quantified Relevance Logic (Journal of Philosophical Logic 17 (1988)).

Once upon a time, modal logic was castigated because it ‘had no semantics.’ Kripke, Hintikka, Kanger, and others changed all that. In a similar way, when Relevant Logic was introduced by Anderson and Belnap, it too was castigated for ‘having no semantics.’ The present overview marks a culmination of that effort. The semantic approach described here brings together a number of hitherto disparate efforts to set out formal systems for logics of relevant implication and entailment. It also makes clear (despite (...) some of our hopes and utterances) that the One True Logic does not exist. This is as true for relevant logics as Kripke et al., showed it to be for modal logics. In both cases, subtle (and not so subtle) variations on semantical postulates produce different logics in the same family. The question of which semantical postulates are correct makes no sense without further context, i.e., the questioner needs to answer the question: Correct for what? The question that does remain is: What motivates the relevant family of logics? And this is the question that is the main job for this chapter to investigate. (shrink)

The Logic R4 is obtained by adding the axiom □ → to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete (...) over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough. (shrink)

This paper presents ConR (Conditional R), a logic of conditionals based on Anderson and Belnap''s system R. A Routley-Meyer-style semantics for ConR is given for the system (the completeness of ConR over this semantics is proved in E. Mares and A. Fuhrmann, A Relevant Theory of Conditionals (unpublished MS)). Moreover, it is argued that adopting a relevant theory of conditionals will improve certain theories that utilize conditionals, i.e. Lewis'' theory of causation, Lewis'' dyadic deontic logic, and Chellas'' dyadic deontic logic.

A theory of ersatz impossible worlds is developed to deal with the problem of counterpossible conditionals. Using only tools standardly in the toolbox of possible worlds theorists, it is shown that we can construct a model for counterpossibles. This model is a natural extension of Lewis's semantics for counterfactuals, but instead of using classical logic as its base, it uses the logic LP.

The doctrine of semantic dialetheism is set out and contrasted with metaphysical dialetheism. We find that there is a lot to be said in favour of semantic dialetheism. Semantic dlaietheism is given credence by the doctrine of partially defined predicates. To make sense of a partially defined predicate, Tappenden and Soames suggest that the seman tics of predicates should be given in terms of a set of conditions under which the predicate can be applied to things and a set of (...) conditions under which its negation can be applied. If Tappenden and Soames are correct that many predicates are partially defined then it is also plausible that some are 'overdefined'. We say that a predicate is overdefined if and only if it is possible that its negative and positive conditions pick out some of the same objects at the same time. Some examples of overdefined predicates are discussed and it is suggested that a semantic dialetheist treatment of some folk theories (such as the folk theory of identity and the folk theory of belief) is appropriate. (shrink)

A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46.

The Logic R4 is obtained by adding the axiom □(A v B) → (◇A v □B) to the modal relevant logic NR. We produce a model theory for this logic and show completeness. We also show that there is a natural embedding of a Kripke model for S4 in each R4 model structure.

RGLis a version of the modal logic GLbased on the relevant logic R. It is shown that the class of RKframes that verify all theorems of RGLalso verify a scheme that we call (!). If RGLhas (!) as a theorem, however, it is not a relevant logic. I go on to show that not all instances of (!) are theorems of RGL, hence this logic is not complete over any class of RKframes.

This chapter contains sections titled: Non‐Sequiturs are Bad The Real Use of Premises Implication From Proof Theory to Semantics Adding Conjunction The Problem of Disjunction Routley and Meyer's Ternary Relation Rules for Disjunction The Semantics of Negation Rules for Negation Disjunctive Syllogism Logics Stronger than R Logics Weaker than R Relevant Logics and Natural Language Conditionals Theory of Properties Summary.

This paper shows that a collection of modal relevant logics are conservatively extended by the addition of Boolean negation.

In reviewing 50 years of personal research on influenza, I have journeyed, literally and figuratively, from an army camp epidemic in Fort Monmouth NJ in 1947 to a (literal and figurative) Valhalla, where I now conduct my research. Having entered the field as a physician, I have always sought practical applications of my work, yet in every instance, such applications have led me to seek further answers in basic research as new questions arose. I entered the area of influenza virus (...) genetics by the back door through an interest in the effects of corticosteroid hormones on viral replication, used the genetic approach in analyzing the morphological variation of the virus and, in so doing, exploited the finding of a linkage of high‐yield growth to spherical morphology. Today, all influenza vaccine viruses are high‐yield genetic reassortants. Subsequent study of reassortant viruses facilitated the identification and isolation of the two major antigens of the virus in antigenic hybrids and showed their differing functions in the induction of immunity. In turn, a new approach to influenza vaccination has been discovered and is presently under clinical investigation. (shrink)

The British Museum, based in Montague House, Bloomsbury, opened its doors on 15 January 1759, as the world's first state-owned public museum. The Museum's collection mostly originated from Sir Hans Sloane, whose vast holdings were purchased by Parliament shortly after his death. The largest component of this collection was objects of natural history, including a herbarium made up of 265 bound volumes, many of which were classified according to the late seventeenth-century system of John Ray. The 1750s saw the emergence (...) of Linnaean binomial nomenclature, following the publication of Carl Linnaeus'Species Plantarum andSystema Naturae. In order to adopt this new system for their collections, the Trustees of the British Museum chose to employ the Swedish naturalist and former student of Linnaeus, Daniel Solander to reclassify the collection. Solander was ordered to devise a new system for classifying and cataloguing Sloane's natural history collection, which would allow both Linnaeans and those who followed earlier systems to access it. Solander's work was essential for allowing the British Museum to realize its aim of becoming a public centre of learning, adapting the collection to reflect the diversity of classificatory practices which were existent by the 1760s. This task engaged Solander until 1768, when he received an offer from Joseph Banks to accompany him on HMSEndeavourto the Pacific. (shrink)

We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to (...) trivialize the semantics. (shrink)

This paper uses an atomistic ontology of universals, individuals, and facts to provide a semantics for ramified type theory. It is shown that with some natural constraints on the sort of universals and facts admitted into a model, the axiom of reducibility is made valid.

Processes of adapting complex information for broad audiences became a pressing concern by the turn of the twentieth century. Channels of communication ranged from public lectures to printed books designed to serve a social class eager for self-improvement. Through analyzing a course of public lectures given by George Howard Darwin (1845–1912) for the Lowell Institute in Boston and the monograph he based on these, The Tides and Kindred Phenomena of the Solar System (1898), this article connects the important practices of (...) public lecturing and book production–two aspects of knowledge dissemination that tend to be studied as separate entities. Darwin, Plumian Professor of Astronomy at the University of Cambridge and son of the famous naturalist, relied on a diverse material culture when lecturing and producing a book. Giving a new account of Darwin’s scientific work through exploring his adaption of it for broader audiences, this article connects the diverse material culture Darwin employed in talks to the practice of producing a published book. The content of objects demonstrated and the lantern slides projected during Darwin’s lectures evolved to form a book designed to engage broad sectors of society in Europe and the United States. Darwin’s lectures were attended at full capacity, while The Tides was soon printed in numerous English editions and translated into German, Italian, Hungarian, and Spanish. (shrink)

This paper uses an "admissible set semantics" to treat quantification in quantified modal logics. The truth condition for the universal quantifier states that a universally quantified statement (x)A(x) is true at a world w if and only if there is some proposition true at that world that entails every instance of A(x). It is shown that, for any canonical propositional modal logic the corresponding admissible set semantics characterises the quantified version of that modal logic.

I have found in teaching courses on philosophy of language that one can concentrate either on the problem of reference or the problem of meaning, not on both and still teach a coherent course. Kenneth Taylor’s Truth and Meaning provides further confirmation of this view. It is a very good textbook for a course on the theory of meaning and attempts to say relatively little about reference. It is clear and well written. It presents a wide range of rather difficult (...) material perhaps as clearly and easily as possible. The most difficult problem in reviewing this book has been to decide what level course or what sort of student would be best served by it. My answer to this is a bit involved and will be left until after I have described the contents of the book. (shrink)

In "An Alternative Semantics for Quantified Relevant Logic" (JSL 71 (2006)) we developed a semantics for quantified relevant logic that uses general frames. In this paper, we adapt that model theory to treat quantified modal logics, giving a complete semantics to the quantified extensions, both with and without the Barcan formula, of every proposi- tional modal logic S. If S is canonical our models are based on propositional frames that validate S. We employ frames in which not every set of (...) worlds is an admissible proposition, and an alternative interpretation of the uni- versal quantifier using greatest lower bounds in the lattice of admissible propositions. Our models have a fixed domain of individuals, even in the absence of the Barcan formula. For systems with the Barcan formula it is possible to preserve the usual Tarskian reading of the quantifier, at the expensive of sometimes losing va- lidity of S in the underlying propositional frames. We apply our results to a number of logics, including S4.2, S4M and KW, whose quantified extensions are incomplete for the standard semantics. (shrink)

We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.