Information Flow In Logics in the Vicinity of BB

Australasian Journal of Logic 18 (1):1-24 (2021)
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Abstract

Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised ver- sion of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB+(^I), which falls between Lavers' system BB+ and B+ , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions).

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Andrew Tedder
University of Connecticut

Citations of this work

Semantic conceptions of information.Luciano Floridi - 2008 - Stanford Encyclopedia of Philosophy.
Neighbourhood Semantics for Quantified Relevant Logics.Andrew Tedder & Nicholas Ferenz - 2022 - Journal of Philosophical Logic 51 (3):457-484.
Neighbourhood Semantics for Modal Relevant Logics.Nicholas Ferenz & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (1):145-181.
A Substructural Approach to Explicit Modal Logic.Shawn Standefer - 2023 - Journal of Logic, Language and Information 32 (2):333–362.

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References found in this work

Semantics for relevant logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
Information flow and relevant logics.Greg Restall - 1996 - In Jerry Seligman & Dag Westerstahl, Logic, Language and Computation. Center for the Study of Language and Inf. pp. 463–477.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1977 - Journal of Symbolic Logic 42 (2):315-316.

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