S. Mantha. First-Order Preference Theories and Their Applications. PhD thesis, University of Utah, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....it is possible to develop realistic proof procedures for special classes of priority theories. In fact, many such procedures exist. Since normal logic programs are a special class of priority logic programs, the elegant proof procedure by Eshghi and Kowalski for abductive reasoning [17] also see [31, 47]) and the various efficient proof procedures for the well founded semantics, can be adopted for the corresponding class of priority logic programs (under the corresponding semantics) Since default theories are a class of priority logic programs, Reiter s backward chaining procedure to prove ....

S. Mantha. First-Order Preference Theories and Their Applications. PhD thesis, University of Utah, 1991.

....Furthermore, the criteria for ordering the solutions have no explicit status in the model theory as the semantics of optimization (when it is discussed) is usually provided through negation [20, 23, 48, 65] 2.1. 3 Logic of Preference The syntax of the logic of preference introduced by Mantha [63] extends the syntax of first order logic by introducing a modal operator P f with the rule of formation: if F is a formula then so is P f F . Following the model tradition in modal logic enunciated by Carnap [15, 16] and Kripke [54, 55] where the possible worlds semantics for modal logic was ....

....of first order logic by introducing a modal operator P f with the rule of formation: if F is a formula then so is P f F . Following the model tradition in modal logic enunciated by Carnap [15, 16] and Kripke [54, 55] where the possible worlds semantics for modal logic was introduced) Mantha [63] provides a possible worlds semantics for preference logic. Essentially, the truth value of purely first order formulae at any world is determined in the usual way, but a formula of the form P f F is true at a world w if every world v where F is true is related to w by the relation , i.e. w v. ....

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S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....well ordering of this kind specifies which defaults should be performed before which others. This is a useful priority constraint, but it is different from ours where the notion of priority constraint means that a rule s application automatically blocks another. Allen Brown et al. 1, 2] also see [14, 19]) propose a family of modal logics of preference where preference is used in selecting models. By introducing the preference, they argue that the resulting theory turns out to be surprisingly general and powerful. In general, the preference logic there is based on two modal operators, P f and P b ....

S. Mantha. first-Order Preference Theories and their Applications. PhD thesis, University of Utah, 1991.

....that are solutions of c( u) Theorem 2 Given a preference logic program P and a relaxable query G, the relaxed intended preference model exists and is unique up to an isomorphism. Proof Sketch: Given a preference logic program P , we can show that it has a unique intended preference model [5, 13]. The relaxed intended preference model for a preference logic program and a relaxable query is a uniquely defined sub frame of the intended preference model of the original program thereby leading to the theorem. Definition 2 Given a preference logic program P , an atom A that depends on a ....

S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....evident how one can perform relaxation in this paradigm. This is the main topic of the present paper. While there has been considerable research on partial constraint satisfaction [3] not much has been done within the framework of logic programming. Two notable efforts are Relaxable Horn Clauses [2, 7] and Hierarchical Constraint Logic Programming [1, 9] Mantha et al. introduced Relaxable Horn Clauses, where a relaxable clause is a definite clause with a partial order over the goals in the body; the partial order dictates the order in which the goals are to be relaxed if all the goals in the ....

S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....has also been studied in other fields including decision theory, economics, philosophical logic, artificial intelligence, and operations research. Recently, von Wright [37] attempted a logical formalization of preference by modeling it as a binary relation amongst propositions. Mantha et al. [5, 28], on the other hand, argued that a more uniform notion of preference is one that makes preference a binary relation amongst states of affairs. He introduced a family of modal logics of preference and showed their use in modeling non monotonic reasoning, deontic logic, etc. 5, 28] Mantha also ....

....Mantha et al. [5, 28] on the other hand, argued that a more uniform notion of preference is one that makes preference a binary relation amongst states of affairs. He introduced a family of modal logics of preference and showed their use in modeling non monotonic reasoning, deontic logic, etc. [5, 28]. Mantha also introduced the notion of preferential theory, with two components: a first order theory and an arbiter. Preferential theories are powerful enough to express a wide variety of constraint optimization problems, which typically have an objective function that specifies the optimal ....

S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....over an appropriate domain. It has been suggested that the preference relation of primary importance is the one between states of affairs (or possible worlds) characterized by possibly infinite sets of propositions. Rather than characterize states of affairs themselves by single propositions, [Man91] suggests that the reason for the betterness of one state of affairs over another be captured by single propositions (preference criteria) Our discussion of preference logics below is based on [Man91, BMW94] Familiarity with modal logic, as described in [Ram88] or [Che80] is sufficient. 2.1 ....

....of propositions. Rather than characterize states of affairs themselves by single propositions, Man91] suggests that the reason for the betterness of one state of affairs over another be captured by single propositions (preference criteria) Our discussion of preference logics below is based on [Man91, BMW94]. Familiarity with modal logic, as described in [Ram88] or [Che80] is sufficient. 2.1 The Modal Logic of Pure Preference P The syntax of P is obtained by extending the syntax of propositional logic L by a monadic modal operator P f , with a corresponding rule of formation: if F is a formula of ....

S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....In this section we introduce the syntax of a preference logic program (henceforth referred to as PLP) and illustrate their use with examples. Just as definite clauses are restricted first order theories, preference logic programs can be viewed as restricted preferential theories, introduced in [10]. 2.1 Syntax A preference logic program has two parts, a first order theory and an arbiter, as described below. The First Order Theory: The first order clauses of a preference logic program can have one of two forms: 1. H B 1 ; B n , n 0) i.e. definite clauses. In general, some of ....

....assume that the Barcan formulae [3] are true, that each function symbol is a rigid functor, that each term is a rigid designator, and the domain over which terms are constructed is the same in all worlds. 3. 1 Preference Logic We now briefly describe the modal logic of preference introduced in [10]. The syntax of this logic extends the syntax of first order logic by adding a new modal operator P f with the associated rule of formation: If F is a formula then so is P f F . Each definite preference clause p( t) p( u) L 1 ; L n is translated into a clause p( t) P f (p( u) ....

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S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

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S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....para : lineLine, paraPara : badness(Badness) Lineparalast(false) Linebadness(Linebadness) Parabadness(Parabadness) Badness = Linebadness Parabadness. paraParabadness(B) Pf(paraPara1badness(B1) B1 B) The symbol Pf is the monadic modal operator of preference introduced in [Man91]. Such rules are called preference rules and specify that the preferred parse from the nonterminal para is the one whose badness property is the least in the ordering . We now turn to an example illustrating how to specify the criteria for resolving ambiguity in context free grammars. Consider ....

S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

....2.1 A preferential model is said to be supported, iff, if for any two worlds w and v if w v, then there exists a formula P f A such that w j= P f A and v j= A. Supported preferential models will be important in the treatment of preferential theories and their intended preference models [8] [21]. There are, however, transitive preference frames where it is not valid. To characterize transitivity exactly, the notion of prohibition introduced in P 2 above is needed. 3 Granularity of Preference The notion of preference is fundamental to computing. From combinatorial optimization to the ....

Mantha, S. First-order preference theories and their applications. Tech. rep., Dept. of Computer Science, University of Utah, 1992.

....simple preference logic programs (without relaxation goals in bodies of clauses) 8] and then extend it to preference logic programs with relaxation goals in the bodies of clauses. 4. 1 Model Theory of Optimization Preference logic programs are viewed as theories in the modal logic of preference [17], and hence the model theory for preference logic programs uses ideas from modal logic. We provide a possible world semantics for preference logic programs where each world is a model for the program and an ordering among the worlds is enforced by the arbiter clauses. We the review of the model ....

....modal logic. We provide a possible world semantics for preference logic programs where each world is a model for the program and an ordering among the worlds is enforced by the arbiter clauses. We the review of the model theory starting with a brief introduction to the modal logic of preference [17]. The syntax of this logic extends the syntax of first order logic by adding a new modal operator Pf with the associated rule of formation: If F is a formula then so is Pf F . We treat each definite preference clause p( t) p( u) L1 ; Ln in a preference logic program as a formula p( ....

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S. Mantha. First-Order Preference Theories and their Applications. PhD thesis, University of Utah, November 1991.

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