
219Conditional assertion and restricted quantification: Abstracts of commentsNoûs 4 (1): 13. 1970.

119Relevance logics and relation algebrasReview of Symbolic Logic 2 (1): 102131. 2009.Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the firstdegree fragment of relevance logics. These results show that some core ideas are sha…Read more

98Contradictory Information: Too Much of a Good Thing (review)Journal of Philosophical Logic 39 (4). 2010.Both I and Belnap, motivated the "BelnapDunn 4valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But the …Read more

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

75Intuitive semantics for firstdegree entailments and 'coupled trees'Philosophical Studies 29 (3): 149168. 1976.

67Kripke models for linear logicJournal of Symbolic Logic 58 (2): 514545. 1993.We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operat…Read more

66Quantum MathematicsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980. 1980.This paper explores the development of mathematics on a quantum logical base when mathematical postulates are taken as necessary truths. First it is shown that firstorder Peano arithmetic formulated with quantum logic has the same theorems as classical firstorder Peano arithmetic. Distribution for firstorder arithmetical formulas is a theorem not of quantum logic but rather of arithmetic. Second, it is shown that distribution fails for secondorder Peano arithmetic without extensionality. Thi…Read more

60Partiality and its dualStudia Logica 66 (1): 540. 2000.This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the fourvalued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's threevalued logic, Kleene's threevalued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the firstdegree fragment of the Dun…Read more

55Canonical Extensions and Relational Completeness of Some Substructural LogicsJournal of Symbolic Logic 70 (3). 2005.In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion

52Positive modal logicStudia Logica 55 (2). 1995.We give a set of postulates for the minimal normal modal logicK + without negation or any kind of implication. The connectives are simply , , , . The postulates (and theorems) are all deducibility statements . The only postulates that might not be obvious are.

49Negation in the Context of Gaggle TheoryStudia Logica 80 (23): 235264. 2005.We study an application of gaggle theory to unary negative modal operators. First we treat negation as impossibility and get a minimal logic system Ki that has a perp semantics. Dunn 's kite of different negations can be dealt with in the extensions of this basic logic Ki. Next we treat negation as “unnecessity” and use a characteristic semantics for different negations in a kite which is dual to Dunn 's original one. Ku is the minimal logic that has a characteristic semantics. We also show that…Read more

47A Kripkestyle semantics for RMingle using a binary accessibility relationStudia Logica 35 (2). 1976.

45A consecutive calculus for positive relevant implication with necessityJournal of Philosophical Logic 9 (4): 343362. 1980.

44Algebraic Methods in Philosophical LogicOxford University Press. 2001.This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects

42A theorem in 3valued model theory with connections to number theory, type theory, and relevant logicStudia Logica 38 (2). 1979.Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (nondegenerate) 3valued counterpart of . Classical sentences that are true in are nonfalse in . Applications to number theory and type theory (with axiom of infinity) produce finite 3valued models in which all classically true sentences of these theories are nonfalse. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic…Read more

41A relational representation of quasiBoolean algebrasNotre Dame Journal of Formal Logic 23 (4): 353357. 1982.

39Symmetric generalized galois logicsLogica Universalis 3 (1): 125152. 2009.Symmetric generalized Galois logics (i.e., symmetric gGl s) are distributive gGl s that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We represent symmetric gGl s by models on topological relational structures. On the other hand, topologic…Read more

39A sieve for entailmentsJournal of Philosophical Logic 9 (1). 1980.The validity of an entailment has nothing to do with whether or not the components are true, false, necessary, or impossible; it has to do solely with whether or not there is a necessary connection between antecedent and consequent. Hence it is a mistake (we feel) to try to build a sieve which will “strain out” entailments from the set of material or strict “implications” present in some system of truthfunctions, or of truthfunctions with modality. Anderson and Belnap (1962, p. 47)

32Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing (review)Journal of Philosophical Logic 42 (3): 443459. 2013.

31A modification of Parry's analytic implicationNotre Dame Journal of Formal Logic 13 (2): 195205. 1972.

30Completeness of relevant quantification theoriesNotre Dame Journal of Formal Logic 15 (1): 97121. 1974.

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

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