A New Approach to Preferential Structures

Schlechta, Karl; Gourmelen, Laurent; Motré, Stéphanie; Rolland, Olivier; Tahar, Bensalah

doi:10.3233/fi-2000-423407

Cited by 5 publications

(4 citation statements)

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“…We have all possibilities in one structure, this expresses scepticism. Alternatively, we may work with many structures in parallel, see [SGMRT00], this corresponds to an extensions approach.…”

Section: Direct Scepticism Vs Intersection Of Extensionsmentioning

confidence: 99%

Equilibria und weiteres Heiteres II

Gabbay,

Schlechta

2011

Preprint

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Heiteres(2) Let X be such a set of formulas. Let X i ⊆ X be the set of formulas in X with length i, i.e., a consistent conjunction of i many propositional variables or their negations, i > 0.As the model sets for X are pairwise disjoint, the model sets for all φ ∈ X i have to be disjoint.(3) It suffices now to show that each X i is at most countable; we even show that each X i is finite. Proof by induction:Consider i = 1. Let φ, φ ′ ∈ X 1 . Let φ be p or ¬p. If φ ′ is not ¬φ, then φ and φ ′ have a common model. So one must be p, the other ¬p. But these are all possibilities, so card(X 1 ) is finite.Let the result be shown for k < i.Consider now X i . Take arbitrary φ ∈ X i . Without loss of generality, let φ = p 1 ∧ . . .) is finite, as all φ ′ ∈ X i,k have to be mutually inconsistent. Thus, card(X i ) is finite. (Note that we did not use the fact that elements from different X i,k , X i,k ′ also have to be mutually inconsistent; our rough proof suffices.) ✷ Note that the proof depends very little on logic. We needed normal forms, and used two truth values. Obviously, we can easily generalize to finitely many truth values.

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Section: Direct Scepticism Vs Intersection Of Extensionsmentioning

confidence: 99%

Equilibria und weiteres Heiteres II

Gabbay,

Schlechta

2011

Preprint

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“…For preferential reasoning (with some relation ∼ | outside the "core language" ), we may again take all classical models -however defined -and introduce the interpretation of ∼ | in the algebraic or abstract superstructure (see below), but we may also consider a normality operator ∇ directly in the language, and all consistent sets of such formulas (see e.g. [SGMRT00]). Our picture is large enough to admit both possibilities.…”

Section: Basic Semantical Entitiesmentioning

confidence: 99%

“…Bookkeeping seems difficult, especially when we have nested operators, which have all to be interpreted in the various ways. In a second step, we can unite all possibilities in one grand picture (a universal structure, as it permits to find exactly all consequences in one construction, and not in several ones as is done for classical logic), essentially by a disjoint union -this was done (more or less) in the authors' [SGMRT00] for preferential structures.…”

Section: Restricted Operators and Relationsmentioning

confidence: 99%

“…We can see the problem of copies also as preservation of ignorance, and can also solve it with many structures -as is done in [SGMRT00]. We have to do this construction now also for other u and U, so we will perhaps introduce copies for other elements, too, suppose we have copies u ′ , y and u ′ , y ′ for the above u ′ .…”

Section: General Preferential Structuresmentioning

confidence: 99%

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Logical tools for handling change in agent-based systems

Gabbay,

Schlechta

2008

Preprint

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The human agent in his daily activity has to deal with many situations involving change. Chief among them are the following (1) Common sense reasoning from available data. This involves predication of what unavailable data is supposed to be (nonmonotonic deduction) but it is a defeasible prediction, geared towards immediate change. This is formally known as nonmonotonic reasoning and is studied by the nonmonotonic community.(2) Belief revision, studied by a very large community. The agent is unhappy with the totality of his beliefs which he finds internally unacceptable (usually logically inconsistent but not necessarily so) and needs to change/revise it.(3) Receiving and updating his data, studied by the update community.(4) Making morally correct decisions, studied by the deontic logic community.(5) Dealing with hypothetical and counterfactual situations. This is studied by a large community of philosophers and AI researchers.(6) Considering temporal future possibilities, this is covered by modal and temporal logic.(7) Dealing with properties that persist through time in the near future and with reasoning that is constructive. This is covered by intuitionistic logic.All the above types of reasoning exist in the human mind and are used continuously and coherently every hour of the day. The formal modelling of these types is done by diverse communities which are largely distinct with no significant communication or cooperation. The formal models they use are very similar and arise from a more general theory, what we might call: "Reasoning with information bearing binary relations". Short overview of the different logicsWe will discuss the semantics of the propositional logic situation only. In all cases except the last two (i.e. Inheritance and Argumentation), the semantics consist of a set of classical models for the underlying language, with an additional structure, usually a binary relation (sometimes relative to a point of origin). This additional structure is not unique, and the result of the reasoning based on this additional structure will largely depend on the specific choice of this structure. The laws which are usually provided (as axioms or rationality postulates) are those which hold for any such additional structure. Nonmonotonic logicsNonmonotonic logics (NML) were created to deal with principled reasoning about "normal" situation. Thus, "normal" birds will (be able to) fly, but there are many exceptions, like penguins, roasted chickens, etc., and it is usually difficult to enumerate all exceptions, so they will be treated in bulk as "abnormal" birds.The standard example is -as we began to describe already -that "normal" birds will (be able to) fly, that there are exceptions, like penguins, that "normal" penguins will not fly, but that there might be exceptions to the exceptions, that some abnormal penguin might be able to fly -due to a jet pack on its back, some genetic tampering, etc. Then, if we know that some animal is a bird, call it "Tweety" as usual, and if we want to keep it as a pet, we sho...

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Logical Tools for Handling Change in Agent-Based Systems

Gabbay

Schlechta

2010

Cognitive Technologies

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A New Approach to Preferential Structures

Cited by 5 publications

References 7 publications

Equilibria und weiteres Heiteres II

Equilibria und weiteres Heiteres II

Logical tools for handling change in agent-based systems

Logical Tools for Handling Change in Agent-Based Systems

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