Semantic analysis of orthologic

Goldblatt, Robert

doi:10.1007/bf00652069

Cited by 227 publications

(153 citation statements)

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“…the logics of modular and distributive bounded lattices and their variations [40]), or its proper language-expansions (e.g. the full Lambek calculus [32], bilattice logic [4], orthologic [35], linear logic [34]). Hence, it is sensible to require of an adequate proof theory of lattice logic to be able to account in a modular way for these logics as well.…”

Section: Towards a Modular Proof Theory For Lattice Logicmentioning

confidence: 99%

Lattice Logic Properly Displayed

Greco

Palmigiano

2017

Logic, Language, Information, and Computation

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We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and subformula property. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main interest and added value of the present proposal, and allows for the smoothest Belnap-style proof of cut-elimination. Our proposal builds on an algebraic and order-theoretic analysis of the semantic environment of lattice logic, and applies the guidelines of the multitype methodology in the design of display calculi.

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Section: Towards a Modular Proof Theory For Lattice Logicmentioning

confidence: 99%

Lattice Logic Properly Displayed

Greco

Palmigiano

2017

Logic, Language, Information, and Computation

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“…For example, consider a form of the pragmatist theory of truth, on which a statement is true if it is currently accepted, but True if society converges on it as something that is accepted for all time. 7 Clearly there will be no con ‡ict between changing negative information and negative truths in this …rst sense, and in the long run no con ‡ict between information and Truth in the second sense. Thus, we can distinguish also between two senses in which information can be available in situations.…”

Section: Negation and The Metaphysics Of Informationmentioning

confidence: 99%

Information, Negation, and Paraconsistency

Mares

2012

Paraconsistency: Logic and Applications

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This paper begins by arguing that a truth conditional approach to the semantics for relevant logic is unnatural. Rather, we should adopt an informational semantics. On this view, the indices in the RoutleyMeyer semantics are situations, which can be said either to contain or not contain, particular pieces of information. Valid inference, then, is seen as information preservation, not truth preservation. The distinction between truth and information gives us some freedom in our treatment of logic. For example, we may have a very classical theory of truth but a very non-clasisical theory of information. On the other hand, we may accept very non-classical theories of truth (such as dialetheism) together with an informational treatment of logic.

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“…In the framework of Rough Sets [23], a reflexive, symmetric, and transitive relation of indistinguishability is called indiscernibility, and if it is only reflexive and symmetric it is called a tolerance relation [29,21]. In addition, their logical status has been well studied and give rise to orthologic [12], and the modal logic system B (see [18]). Further, in the usual modal logics of belief reflexivity is dropped, as the agent may distinguish her present state from the one she believes (falsely) that she is in.…”

Section: A > B Is True At a State S Iff The Closest A-world To S Is Amentioning

confidence: 99%