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23Generalized onrno negationIn Heinrich Wansing (ed.), Negation: a notion in focus, W. De Gruyter. pp. 7--3. 1996.
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51A 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 truth-functions, or of truth-functions with modality. Anderson and Belnap (1962, p. 47)
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49Algebraic completeness results for r-Mingle and its extensionsJournal of Symbolic Logic 35 (1): 1-13. 1970.
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52A modification of Parry's analytic implicationNotre Dame Journal of Formal Logic 13 (2): 195-205. 1972.
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47New Consecution Calculi for R→tNotre Dame Journal of Formal Logic 53 (4): 491-509. 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 Gentzen-style 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
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96Relevant predication 1: The formal theory (review)Journal of Philosophical Logic 16 (4): 347-381. 1987.
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82Negation in the Context of Gaggle TheoryStudia Logica 80 (2): 235-264. 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
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125Contradictory Information: Too Much of a Good Thing (review)Journal of Philosophical Logic 39 (4). 2010.Both I and Belnap, motivated the "Belnap-Dunn 4-valued 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
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 |