Size and Logic

Gabbay, Dov M.; Schlechta, Karl

doi:10.1017/s1755020309090224

Cited by 9 publications

(34 citation statements)

References 10 publications

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“…The first time that abstract size was related to non-monotonic logics was, to our the best of knowledge, in the second author's [Sch90] and [Sch95-1], and, independently, in [BB94]. More detailed remarks can also be found in [GS08c], [GS09a], and [GS08f]. More detailed remarks can also be found in [GS08c], [GS09a], and [GS08f].…”

Section: Various Concepts Of Size and Non-monotonic Logicsmentioning

confidence: 94%

“…Most of the material of this chapter (unless marked as "new") was published previously; see [Sch04], [GS08b], [GS08c], [GS09a], and [GS08f]. In addition, we also want to put our work a bit more in perspective, and make it self-contained, for the convenience of the reader.…”

Section: Basic Definitionsmentioning

confidence: 99%

“…The connection between non-monotonic logic and the abstract concept of size was investigated in [GS09a] (see also [GS08f]). There, we looked among other things at abstract addition of size.…”

Section: Interpolation and Sizementioning

confidence: 99%

“…All parts of Chapter 2 (page 31) which are not marked as new material were published in some of [Sch04], [GS08b], [GS08c], [GS09a], [GS08f].…”

Section: Previously Published Material Acknowledgementsmentioning

confidence: 99%

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Conditionals and Modularity in General Logics

Gabbay¹,

Schlechta²

2011

Cognitive Technologies

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Section: Various Concepts Of Size and Non-monotonic Logicsmentioning

confidence: 94%

Section: Basic Definitionsmentioning

confidence: 99%

Section: Interpolation and Sizementioning

confidence: 99%

“…All parts of Chapter 2 (page 31) which are not marked as new material were published in some of [Sch04], [GS08b], [GS08c], [GS09a], [GS08f].…”

Section: Previously Published Material Acknowledgementsmentioning

confidence: 99%

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Conditionals and Modularity in General Logics

Gabbay¹,

Schlechta²

2011

Cognitive Technologies

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“…For general references on tableaux and on modal tableaux, see [1,[3][4][5]20]. For general papers on Reactivity and its use see [2,6,7,10,11,[13][14][15][16][17][18][19].…”

Section: Setting the Scenementioning

confidence: 99%

Introducing Reactive Modal Tableaux

Gabbay

2013

Reactive Kripke Semantics

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This paper introduces the idea of reactive semantics and reactive Beth tableaux for modal logic and quotes some of its applications. The reactive idea is very simple. Given a system with states and the possibility of transitions moving from one state to another, we can naturally imagine a path beginning at an initial state and moving along the path following allowed transitions. If our starting point is s 0 , and the path is s 0 , s 1 , . . . , s n , then the system is ordinary non-reactive system if the options available at s n (i.e., which states t we can go to from s n ) do not depend on the path s 0 , . . . , s n (i.e., do not depend on how we got to s n ). Otherwise if there is such dependence then the system is reactive. It seems that the simple idea of taking existing systems and turning them reactive in certain ways, has many new applications. The purpose of this paper is to introduce reactive tableaux in particular and illustrate and present some of the applications of reactivity in general. Mathematically one can take a reactive system and turn it into an ordinary system by taking the paths as our new states. This is true but from the point of view of applications there is serious loss of information here as the applicability of the reactive system comes from the way the change occurs along the path. In any specific application, the states have meaning, the transitions have meaning and the paths have

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