James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--130, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of confidence (and a somewhat similar concept of a default) to that in circumscription, including: the specificity dominance principle employed in inheritance, e.g. cf. Touretzky, 1986] Stein, 1989] Quantz and Royer, 1992] Geffner, 1992] conditional logics, e.g. cf. Delgrande, 1987a] Delgrande, 1987b] Geffner, 1992] and argument systems, e.g. cf. Loui, 1987] aggregation principles for modelpreference logics [Brown and Shoham, 1989] including for logic programming with negation as failure [Przymusinski, 1988] and terminological logics [Quantz and Royer, 1992] possibilistic logic ....

James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--130, 1987.

....conditional connectives are allowed only in the consequent of conditional formulas. This restriction arises naturally out of the deontic, and in general defeasible logic, literature. Almost all logics for defeasible conditionality use only the flat (i.e. non nested) part of CL, see e.g. [Alc93,Bel90,Bel91,Del87,Del88,Han69,KLM90,Lam91,Leh89]) and some admit iteration of the conditional connective only in the consequent of conditional formulas (this is the case with [CT92] s four valued conditional logic for knowledge update and [GMS96] s treatment of hypothetical logic programming) As we shall see, this restriction has its pros ....

....e#cient tableau proof system for CLs. GD88] and [Lam92] are already steps in this direction. Groeneboer and Delgrande [GD88] present a method for constructing Kripke models for CL which generalizes Hughes and Cresswell s [HC68] method of semantic diagrams for the modal logic S4.3 to Delgrande s [Del87] conditional logic NP . This extension is made possible by the correspondence between S4.3 and NP [Bou94] However, to exploit this correspondence (via Kripke models for normal modal logics) we have to consider only the flat part of NP ; conditional formulas allowing iterated conditionals in the ....

James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33: 105--139, 1987.

....Katsuno and Satoh [28] whose analysis rely on Kripke structures very close to Kraus, Lehmann and Magidor s preferential models. In particular, Boutilier [8] has shown on this basis that Kraus, Lehmann and Magidor s [29, 31] preferential and rational consequence relation systems and Degrande s [15] logic N closely correspond to the flat parts of modal CLs definitionally equivalent to the standard modal systems S4 and S4.3. In this paper we follow Farinas del Cerro s advice in order to develop a general and effective computation . of nonmonotonic inference relations via automated ....

....other than those they have been devised for. 7 Comparison with Other Works Groeneboer and Delgrande [26] present a method for constructing Kripke models for CLs which generalizes Hughes and Cresswell s [27] classical method of semantic tableau diagrams for the modal logic S4.3 to Delgrande s [15] conditional logic N. This extension is made possible by the correspondence between S4.3 and N. However, as Boutilier [8] has shown, N fails to validate the rule of Cautious Monotonicity, and thus it lies outside the scope of Gabbay s [18] minimal conditions for nonmonotonic consequence relations. ....

James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--139, 1987.

....for future work. 7 Related Work In this section, we consider some work on complexity issues for related subjects. 7. 1 Conditional Modal Logics A stream of semantics for conditional knowledge bases, which we have not considered in this paper, is inherited from conditional modal logics, cf. [26, 27, 14, 15, 59, 36]. Roughly speaking, in these approaches a conditional statement is true at a world w in a set of possible worlds W , if is true in a set f(w; of selected worlds in which is true. The worlds f(w; may be the least exceptional, most normal, etc worlds from the view of w. To capture these ....

....in which no nesting of is allowed, and no connective occurs inside the scope of another connective. The work of Boutilier gives a deep study of modal conditional logics of normality [14, 16, 15] which goes beyond Delgrande s early work on formalizing default reasoning through this approach [26]. Boutilier presented in [14] a conditional logic CT4D, which is equivalent to the modal logic S4.3 and whose flat fragment corresponds to a slight extension of rational consequence in [61] In his later work [16] he introduced conditional logics CT4O and CO and showed that, in our terminology, ....

J. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33(1):105--130, 1987.

....by Boutilier [4] and Katsuno and Satoh [15] rely on Kripke structures very close to Kraus, Lehmann and Magidor s preferential models. In particular, Boutilier [4] has shown on this basis that Kraus, Lehmann and Magidor s [16,18] stronger consequence relation systems P and R and Degrande s [7] logic N closely correspond to the flat parts of modal CLs definitionally equivalent to the standard modal systems S4 and S4.3. In LDS the usual modal semantics is incorporated in the syntactic label construction and only minor variations are needed to pass from a logic to another [1,3,12] So, ....

....for the equivalence test and Corollary 22. 6 Comparison with Other Works Groeneboer and Delgrande [13] present a method for constructing Kripke models for CLs which generalizes Hughes and Cresswell s [14] classical method of semantic tableau diagrams for the modal logic S4.3 to Delgrande s [7] conditional logic N. This extension is made possible by the correspondence between S4.3 and N. However, as Boutilier [4] has shown, N fails to validate the rule of Cautious Monotonicity, and thus it lies outside the scope of Gabbay s [10] minimal conditions for nonmonotonic consequence relations. ....

James P. Delgrande. A First-Order Conditional Logic for Prototypical Properties. Artificial Intelligence, 33:105--139, 1987.

....7 Related Work In this section, we consider some work on complexity issues for related subjects. INFSYS RR 1843 00 06 7. 1 Conditional Modal Logics A stream of semantics for conditional knowledge bases, which we have not considered in this paper, is inherited from conditional modal logics, cf. [26, 27, 14, 15, 59, 36]. Roughly speaking, in these approaches a conditional statement is true at a world w in a set of possible worlds W , if is true in a set f(w; of selected worlds in which is true. The worlds f(w; may be the least exceptional, most normal, etc worlds from the view of w. To capture these ....

....in which no nesting of is allowed, and no connective occurs inside the scope of another connective. The work of Boutilier gives a deep study of modal conditional logics of normality [14, 16, 15] which goes beyond Delgrande s early work on formalizing default reasoning through this approach [26]. Boutilier presented in [14] a conditional logic CT4D, which is equivalent to the modal logic S4.3 and whose flat fragment corresponds to a slight extension of rational consequence in [61] In his later work [16] he introduced conditional logics CT4O and CO and showed that, in our terminology, ....

J. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33(1):105--130, 1987.

....interpret such a counterfactual in a slightly dioeerent way. The conditional clause may refer to, situations which are most normal according to the main clause. With this understanding, the above sentence may also be read iNormally, if it is the case that, j. This direction has been exploitet by [18, 19]. The language of conditional logic is the language of propositional logic augmented by a new binary operator = The following minimal axiom system is included in all conditional logics. Denition 5.31 (System CK) The minimal normal conditional Logic CK is the smallest system which contains the ....

....Nonmonotonic Logics 36 RCEA from ff fi derive (ff = fl) fi = fl) RCK from fi 1 fi 2 : fi n fi derive ( ff fi 1 ) ff fi 2 ) ff fi n ) ff = fi) Lewis [58] has used another system, V in order to capture revision. The system V has also been used by Degrande [18] for dealing with normality. Denition 5.32 (System V) The system V is the smallest system containing CK and the following axioms: ID ff = ff CSO ( ff = fi) fi = ff) ff = fl) fi = fl) CA ( ff = fl) fi = fl) ff fi) fl) CV ( ff = fl) ff = fi) ff fi) ....

J.P. Delgrande. A First-Order Conditional Logic for Prototypical Prperties. Articial Intelligence, no.36, pages 63-90, 1988.

....In this paper, we have established a sharp picture of the complexity of major approaches to default reasoning from conditional knowledge bases. A stream of semantics for conditional knowledge bases that we have not considered in this paper is inherited from conditional modal logics, cf. [15, 16, 8, 42, 21]. Roughly speaking, evaluates in a Lewis style system at a world w to true, if in a set of selected worlds in which is true (the most plausible, least exceptional ones etc) also is true. Such logics allow nested use of , which is not the case in conditional knowledge bases. For example, ....

J. Delgrande. A first-order conditional logic for prototypical properties. Artificial intelligence, 33(1):105--130, 1987. 32 INFSYS RR 1843-99-10

....exception of [Lev90, Lak93] We will first present an an overview of the two conditional logics on which we base this work. 2 Conditional Logics of Normality Recent work in non monotonic reasoning has led to the development of some conditional theories of default inferencing such as the logic N [Del87], ffl entailment [Pea88] preferential entailment [KLM90] CT4O and CO [Bou94] among others. These conditional logics have a minimal set of properties that ought to be common to all non monotonic inference systems and that constitue, as has been suggested by Pearl [Pea89] a conservative core of ....

....the logic CO , since it is not possible to construct a structure where all possible B worlds are present and where the 2 relation is totally connected. Conditional logics can be seen as a core non monotonic logic, to which some extra logic features are added to strengthen the logic. For example, [Del87] adds to a conditional theory a set of formulas that cannot be proven false in ordered to deal with the irrelevance problem. Similar extra logic extensions are proposed in [Bel90, Del94] We believe that the two epistemically extended conditional logics developed here could be amenable for such ....

J.P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33(1):105--130, 1987.

....believe about a lottery that any particular individual typically does not win the lottery. Thus we get 8x(true :Winner(x) 1) However, we believe that typically someone does win the lottery, that is true 9xWinner(x) 2) Unfortunately, in many of the standard approaches, such as Delgrande s [4] version of first order preferential structures, from (1) we can conclude true 8x( Winner(x) 3) Intuitively, from (1) it follows that in the most preferred worlds, each individual d does not win the lottery. Therefore, in the most preferred worlds, no individual wins. This is exactly what (3) ....

J. P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--130, 1987.

....of these distinctions on recognition and prediction problems are presented. Examples from a running system are given. Using a default and abductive reasoning system 2 1 Introduction There have been many proposals for how to build nonmonotonic reasoning systems [Reiter80, McCarthy86, Moore85, Delgrande87] There have, however, been very few discussions as to how one should use a non monotonic reasoning system to solve the sorts of problems we want to solve (notable exceptions are plan recognition in [Kautz87] inheritance systems in [Etherington87] and the use of the abnormality predicate in ....

J. P. Delgrande, "A First-Order Conditional Logic for Prototypical Properties" Artificial Intelligence, Vol. 33, No. 1, pp. 105130.

....evidence to the contrary. Deduction in standard logic does not allow such reasoning; if some proposition follows from a set of axioms, it follows from a superset of the axioms. There have been many proposals for incorporating default reasoning in logic [ Reiter, 1980, McCarthy, 1986, Moore, 1985, Delgrande, 1987, Poole, 1988 ] I assume we use default reasoning to predict what is true. In this paper we consider the problem of default reasoning, and discuss different choices that could be made in developing a default reasoning system. A set of examples is presented which indicates that current default ....

J. P. Delgrande, "A first-order conditional logic for prototypical properties", Artificial Intelligence, Vol. 33, No. 1, 105-130.

....shedding light on an intriguing informal slogan, put forward in philosophy, according to which knowledge is belief that is stable with respect to the truth. 6. The partial order based construction creates a tie with work on preference based nonmonotonic logics [Sho88, KLM90] conditional logics [Lew73, Del87, Bou92a, KS91], and belief revision [KM91] In particular, we are able to show that our construction strictly generalizes a Boutilier s conditional based construction. A couple of our insights turn out to be rediscovery of ideas already published in philosophy (but which are new to computer science and AI) ....

James P. Delgrande. A first order conditional logic for prototypical properties. JAI, (33):105--130, 1987.

.... of confidence (and a somewhat similar concept of a default) to that in circumscription, including: the specificity dominance principle employed in inheritance, e.g. cf. Touretzky, 1986] Stein, 1989] Quantz and Royer, 1992] Geffner, 1992] conditional logics, e.g. cf. Delgrande, 1987a] Delgrande, 1987b] Geffner, 1992] and argument systems, e.g. cf. Loui, 1987] aggregation principles for modelpreference logics [Brown and Shoham, 1989] including for logic programming with negation as failure [Przymusinski, 1988] and terminological logics [Quantz and Royer, 1992] possibilistic logic ....

James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--130, 1987.

.... agent s) default beliefs about default beliefs include non monotonic (NM) modal logics, such as Autoepistemic Logic (AEL) Moore, 1985 ] its predecessor [ McDermott and Doyle, 1980 ] and its offshoots, e.g. Konolige, 1988b ] and [ Levesque, 1990 ] and NM conditional logics, such as [ Delgrande, 1987 ] AEL is highly oriented towards the issues of introspection, e.g. nesting of belief, as traditionally formulated in modal logics of belief and knowledge. In addition, some recent work has addressed issues of multiple agent non monotonic reasoning (NMR) using AEL [ Morgenstern, 1990 ] ....

James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--130, 1987.

....or skeptical, upwards or downwards, and on path preempting inheritance, but no attempts have been made to generalize these approaches to cover more than the individual system licensed. Interestingly, these approaches have all been developed using conditional logics as a starting point. Delgrande (1987) provided a conditional logic called N as a basis for limited reasoning with and about first order defaults. This work was extended by Delgrande (1988) to admit general chaining of defaults through making additional assumptions about the models. Delgrande (1990) provides an algorithm for ....

....have said in Chapter One, I adopt the channel theoretic approach because it provides a convenient ontology for detailing precisely and perspicuously a parameterized semantics for inheritance. Delgrande Boutilier conditional logic The main idea behind the conditional logic approach to defaults (Delgrande, 1987, 1988, 1990) is to use a modal logic with a conditional operator ) where A ) B means, Unless there is an exceptional state of affairs, if A then B. Delgrande develops a first order modal system (which is thus able to represent strict as well as default information using the modal necessity ....

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Delgrande, J. (1987). A First-Order Conditional Logic for Prototypical Properties.

....Much effort in artificial intelligence has been directed toward the development of logic based approaches for interpreting, representing, and reasoning with and about typicality statements. A variety of formalisms have been proposed including, but not limited to, Delgrande s conditional logic[4], 5] McDermott and Doyle s NML[21] Reiter s Default Logic (DL) 36] McCarthy s circumscription[17] Poole s hypothetical reasoning framework[32] and Schlechta s treatment of defaults as generalized quantifiers[37] 1 Each of these formalisms treats typicality statements which henceforth we ....

....default treatments the problem does surface in these other approaches as well. We first noticed the need for denials of defaults in exploring the issue of range defaults [23] In that and other papers [24, 25] we have continued to investigate denials. Several other researchers (Delgrande [4, 5], Poole [32] Schlechta [37] have independently studied default denials. In section 3 we present our treatment of reasoning based on individual inference stand ins, and then show in section 4 that this treatment is subject to substantial difficulties, specifically regarding the representation of ....

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J. P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33(1):105--130, 1987.

....statements. Having distinguished between these two types of conditionals, we can ascribe semantics to each of them using any one of the standard approaches. There have been previous attempts to formalize firstorder conditional logic; some are the natural extension of some propositional formalism (Delgrande 1987; Brafman 1991) while others use alternative approaches (Lehmann Magidor 1990; Schlechta 1995) We defer a detailed discussion of these approaches to the full paper; see also Section 5. How do we make sense of this plethora of alternatives Rather than investigating them separately, we use a ....

....discussed by Poole (1991) As Poole showed, any logic of defaults that satisfies certain minimal properties properties which are satisfied by all the logics we consider is bound to suffer from his version of the lottery paradox. Unfortunately, in many of the standard approaches, such as Delgrande s (1987) version of first order preferential structures, from (1) we can conclude true 8x( Winner(x) 3) Intuitively, from (1) it follows that in the most preferred worlds, each individual d does not win the lottery. Therefore, in the most preferred worlds, no individual wins. This is exactly what (3) ....

Delgrande, J. P. 1987. A first-order conditional logic for prototypical properties. Artificial Intelligence 33:105--130.

....such a counterfactual in a slightly different way. The conditional clause may refer to, situations which are most normal according to the main clause. With this understanding, the above sentence may also be read Normally, if it is the case that, This direction has been exploitet by [18, 19]. The language of conditional logic is the language of propositional logic augmented by a new binary operator = The following minimal axiom system is included in all conditional logics. Definition 5.31 (System CK) The minimal normal conditional Logic CK is the smallest system which contains the ....

....Nonmonotonic Logics 36 RCEA from ff fi derive (ff = fl) fi = fl) RCK from fi 1 fi 2 : fi n fi derive ( ff fi 1 ) ff fi 2 ) ff fi n ) ff = fi) Lewis [58] has used another system, V in order to capture revision. The system V has also been used by Degrande [18] for dealing with normality. Definition 5.32 (System V) The system V is the smallest system containing CK and the following axioms: ID ff = ff CSO ( ff = fi) fi = ff) ff = fl) fi = fl) CA ( ff = fl) fi = fl) ff fi) fl) CV ( ff = fl) ff = fi) ff fi) ....

J.P. Delgrande. A First-Order Conditional Logic for Prototypical Prperties. Artificial Intelligence, no.36, pages 63-90, 1988.

.... this way is the basis for a statistical approach to default reasoning [ Bacchus, 1990; Bacchus, 1989 ] 19 The fact that many non monotonic formalisms allow both of these statements to be asserted without contradiction has been noted, and cited as a weakness, by both Touretzky et al. 1987] and Delgrande [1987]. Gamma Gamma Gamma Gamma Gamma Gamma Gamma Gamma Psi X 1 R X 2 R X 3 Gamma Gamma Gamma Gamma Gamma Gamma Gamma Gamma Psi X 4 Figure 1: A Bayes net Example 8 [Bayesian Networks] Consider the Bayes net in Figure 1. If all of the variables X 1 ....

James P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33:105--130, 1987.

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