Journal of Logic and Computation 26 (5):1617–1636 (2016)

Authors
Thomas Ferguson
City University of New York
Abstract
In this article, we consider variations of Nuel Belnap’s ‘artificial reasoner’. In particular, we examine cases in which the artificial reasoner is faulty, e.g. situations in which the reasoner is unable to calculate the value of a formula due to an inability to retrieve the values of its atoms. In the first half of the article, we consider two ways of modelling such circumstances and prove the deductive systems arising from these two types of models to be equivalent to Graham Priest’s first-degree entailment with an ‘emptiness’ value and Richard Angell’s analytic containment, making computational interpretations of these systems possible. The Belnap-type semantics for AC bring FDE φ and AC in line with other containment logics in their neighborhood. The second half of the article examines formal questions, such as whether AC admits an analysis along the lines of that given to the related system of William Parry’s system of analytic implication, as suggested by Kurt Gödel and confirmed by Kit Fine. Furthermore, a natural means of extending these systems to languages with an intensional implication connective is investigated.
Keywords analytic implication  propositional logic  first-degree entailment  analytic containment
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References found in this work BETA

Angellic Content.Kit Fine - 2016 - Journal of Philosophical Logic 45 (2):199-226.
Grounding and Truth-Functions.Fabrice Correia - 2010 - Logique Et Analyse 53 (211):251-279.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - Journal of Philosophical Logic 44 (1):65-80.

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Citations of this work BETA

Angellic Content.Kit Fine - 2016 - Journal of Philosophical Logic 45 (2):199-226.
On the Logic of Factual Equivalence.Fabrice Correia - 2016 - Review of Symbolic Logic 9 (1):103-122.
Conjunction and Disjunction in Infectious Logics.Hitoshi Omori & Damian Szmuc - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Berlin: Springer. pp. 268-283.
Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.

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