Intuitive semantics for first-degree entailments and ?coupled trees?

Dunn, J. Michael

doi:10.1007/bf00373152

Cited by 489 publications

(167 citation statements)

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“…Our impossible worlds, then, would be like the worlds used in relevant logics such as Belnap and Dunn's First Degree Entailment (Dunn 1976;Belnap 1977): worlds which can be locally glutty or gappy, but are always adjunctive and prime. Now it is intuitive that the contents of our acts of imagination ought to be underdetermined.…”

Section: The Under-determinacy Of Imaginationmentioning

confidence: 99%

Impossible Worlds and the Logic of Imagination

Berto

2017

Erkenn

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I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario-a configuration of objects and properties-correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics.

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Section: The Under-determinacy Of Imaginationmentioning

confidence: 99%

Impossible Worlds and the Logic of Imagination

Berto

2017

Erkenn

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“…The introduction of SIXTEEN 3 in Shramko and Wansing [8] was motivated by a wish to generalise the well-known four-valued Belnap-Dunn logic (Belnap [1,2], Dunn [3]). The latter is based on the values T = {1} (true and not false), F = {0} (false and not true), N = ∅ (neither true nor false), and B = {0, 1} (both true and false) and can be viewed as a generalisation of classical logic-a move from {0, 1} with its usual ordering to P({0, 1}) with two lattice orders.…”

Section: The Trilattice Sixteenmentioning

confidence: 99%

“…Both Shramko and Wansing's original logic and our extension are based on the trilattice SIXTEEN 3 and PL 16 can capture three semantic entailment relations, |= t , |= f , and |= i , that each correspond to one of SIXTEEN 3 's three lattice orderings. 1 The calculus has a relatively simple formulation-only one rule scheme is needed for each of the three negations present in the logic, while each of the three conjunctions and each of the three disjunctions comes with two rule schemes.…”

Section: Introductionmentioning

confidence: 99%

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Interpolation in 16-Valued Trilattice Logics

Muskens

Wintein

2017

Stud Logica

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Abstract.In a recent paper we have defined an analytic tableau calculus PL16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXT EEN 3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic-such as the relations | =t, | = f , and | =i that each correspond to a lattice order in SIXT EEN 3; and | =, the intersection of | =t and | = f . It turns out that our method of characterising these semantic relations-as intersections of auxiliary relations that can be captured with the help of a single calculus-lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L tf , the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano.

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“…Here we will use yet another, a four-valued logic credited to Dunn [2] and to Belnap [1]. This is a multiple-valued logic that contains Kleene's strong three-valued logic as a natural sub-logic (and in a certain sense Kleene's weak three-valued logic as well -see [7]).…”

Section: Logicmentioning

confidence: 99%

A Theory of Truth that Prefers Falsehood

Fitting

1997

Journal of Philosophical Logic

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We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to have many nice features. It is noted that a similar class of fixed points, preferring truth, can also be studied. The notion of intrinsic is shown to relativize to these two subclasses. The mathematical ideas presented here originated in investigations of so-called stable models in the semantics of logic programming.

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Intuitive semantics for first-degree entailments and ?coupled trees?

Cited by 489 publications

References 7 publications

Impossible Worlds and the Logic of Imagination

Impossible Worlds and the Logic of Imagination

Interpolation in 16-Valued Trilattice Logics

A Theory of Truth that Prefers Falsehood

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