
13Truth or Consequences (edited book)Kluwer Academic Publishers. 1990.This collection of essays was compiled for the occasion of Nuel Belnap's 60th birthday.

13Combinators and structurally free logicLogic Journal of the IGPL 5 (4): 505537. 1997.A 'Kripkestyle' semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the TourleyMeyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for 'combinatory posets.' A philosophical interpretation is given of the models, showing that an element of a combinatory poset can be understood simultaneously as a set of states and as a set of actions on states. This …Read more

2Two Manuscripts, One by Routley, One by Meyer: The Origins of the RoutleyMeyer Semantics for Relevance LogicsAustralasian Journal of Logic 15 (2): 171209. 2018.A ternary relation is often used nowadays to interpret an implication connective of a logic, a practice that became dominant in the semantics of relevance logics. This paper examines two early manuscripts  one by Routley, another by Meyer  in which they were developing settheoretic semantics for various relevance logics. A standard presentation of a ternary relational semantics for, let us say, the logic of relevant implication R is quite illuminating, yet the invention of this semantics …Read more

28Fourvalued LogicNotre Dame Journal of Formal Logic 42 (3): 171192. 2001.Fourvalued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction and its residuals can be added to the sequent calculus straightforwardly. We extend a simplified version of t…Read more

9FrontmatterIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.

Chapter VII. Individual quantificationIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 70128. 2017.

Summary review of volume IIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.

5Chapter XII. Applications and discussionIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 488564. 2017.

4Chapter XI. functions, arithmetic, and other special topicsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 392487. 2017.

Index of namesIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 711718. 2017.

3Chapter IX. semanticsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 142266. 2017.

2Analytical table of contentsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.

7Chapter X. proof theory and decidabilityIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 267391. 2017.

8AcknowledgmentsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.

Special symbolsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 747749. 2017.

1ContentsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.

PrefaceIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. 2017.

5Chapter VI. the theory of entailmentIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 169. 2017.

2Chapter VIII. Ackermann's strenge implikationIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 129141. 2017.

4Index of subjectsIn J. Michael Dunn, Nuel D. Belnap & Alan Ross Anderson (eds.), Entailment, Vol. Ii: The Logic of Relevance and Necessity, Princeton University Press. pp. 719746. 2017.

27Relevant predication 3: essential propertiesIn J. Dunn & A. Gupta (eds.), Truth or Consequences, Kluwer Academic Publishers. pp. 7795. 1990.

5A logical framework for the notion of natural propertyIn John Earman & John Norton (eds.), The Cosmos of Science, University of Pittsburgh Press. pp. 6458. 1997.

93Dualling: A critique of an argument of Popper and MillerBritish Journal for the Philosophy of Science 37 (2): 220223. 1986.

15New Consecution Calculi for $R^{t}_{\to}$Notre Dame Journal of Formal Logic 53 (4): 491509. 2012.The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzenstyle calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\m…Read more

2Rmingle and beneath. Extensions of the RoutleyMeyer semantics for RNotre Dame Journal of Formal Logic 20 (n/a): 369. 1979.
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Computing and Information 
Areas of Interest
Philosophy of Mind 
Philosophy of Cognitive Science 
Philosophy of Mathematics 