Shoham, Y.: Nonmonotonic Logics: Meaning and Utility, In: J. McDermott (ed.), Proc. 10th International Joint Conference on Artificial Intelligence, IJCAI-87, Morgan Kaufmann, 1987, pp. 388-393  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... can be written either at the level of the possible alternative sets of beliefs that are the intended outcomes, or at the level of reasoning patterns to construct these outcomes (or both) The first type of specifications at least covers approaches such as preferential semantics (cf. SHO 87] and the notion of S expansions for modal nonmonotonic logics (cf. MT 93] The second type at least covers approaches like default logic (cf. REI 80] The general specification framework (and its semantics) introduced here provides a unifying perspective on these and other well known ....

....consequence: the syntactical form in which the initial facts are given, is not important. Belief state operator for preferential semantics Level 1 semantically consists of descriptions of nonmonotonic reasoning using belief state frames. As an example we consider preferential semantics (cf. SHO 87] Let a preference relation on Mod be given. A belief state operator (with single belief states) can be defined in the following manner: for each X L (X) m Mod m is minimal in Mod(X) Preferential semantics essentially provides a level 1 description, abstracting from ....

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Shoham, Y.: "Nonmonotonic Logics: Meaning and Utility", in: J. McDermott (ed.), Proc. 10th International Joint Conference on Artificial Intelligence, IJCAI-87, Morgan Kaufmann, 1987, pp. 388-393.

....infix notation. Definition 2 (Value minimal) Let T be a theory, let F be a function and Z a tuple of predicate function constants in the language of T . Let R be a partial order defined over the elements of the universe. For two models M and M 0 of 3 Please refer to Lifschitz [6] and Shoham [12] for a general discussion and results on preferential models. 4 This is possible in presence of (i) explicit domain property (each element of the domain has a name) and (ii) categoricity of the ordering defined within the theory. 7 T , we say M (F ;R) Z M 0 if (i) jM j = jM 0 j; ii) ....

Y. Shoham. Nonmonotonic logics: meaning and utility. Proc. the of 10th IJCAI Conference, (1987) 388--393. 29

....preferred models 3.1 Preferred models Here, we add to the classical propositional logic a preference relation between the D interpretations. Let S be a set of symbols, let D S. Let OE be a strict partial order on the set of D interpretations. If D = S, we recover preferential entailment (see [12] for more details) Let M1 ; M2 2 ID , M1 OE M2 means that the D interpretation M2 is strictly preferred over the D interpretation M1 . Thus, we can define a semantics for this new logic: ffl Preferred D interpretations of a set F of D interpretations: the preferred D interpretations of F are the ....

Y. Shoham, `Nonmonotonic logics : Meaning and utility', in IJCAI, pp. 388--393, (1987). Logic Programming, Theorem Proving and Search 354 T. Castell, C. Cayrol, M. Cayrol, D. Le Berre

....which preference information is abduced by an observation. Thus, preference abduction is used for revising a PLP; when new information arrives at a PLP, preference abduction can produce new priorities. Commonsense (nonmonotonic) reasoning and reasoning with priorities are closely related. Shoham [51] argues that the non standard behavior of nonmonotonic reasoning is due to preference mechanisms within it. According to Shoham, nonmonotonic logics are the result of associating a standard logic with a preference relation on models . Examples of research along this line are [13,56,9] Using the ....

Y. Shoham, Nonmonotonic logics: meaning and utility, in: Proceedings of the 10th International Joint Conference on Artificial Intelligence (Morgan Kaufmann, Los Altos, CA, 1987) 388--393.

....(#) is a set of formulas from #, the set of defaults from S. A # specification (A, D) is a specification (#, A, D) Xi The semantics of a specification is a relation on the models of its axioms, representing that some of these models are better than other since they satisfy more of the defaults ([22, 34, 7]) This relation is a pre order. Definition 3 A pre order (from I) is a triple R = #, M,#) where # # Sign I is a signature from I, M # Mod I (#) is a class of interpretation structures of the signature #, # # MM is a reflexive and transitive relation among those interpretation ....

....equivalence class [m] of S # is called an extension of S. A formula belonging to all extensions of S is called a skeptical consequence of S. A formula belonging to some extension of S is called a credulous consequence of S. The usual notion of consequence is the notion of skeptical consequence ([22, 34, 21]) The notion of credulous consequence, introduced in [24] is important in the context of abduction ( 23] We do not commit to one or the other since both can be derived from the chosen semantics. Theories and Galois Connection The theory of a specification S is a special representative of the ....

Y. Shoham. Nonmonotonic logics: meaning and utility. In Proceedings of IJCAI-87, pages 388--392, Milan, 1987. 15

....[ Reiter and Criscuolo, 1981 ] However, representing such dependencies explicitly in rules is inconvenient, and complicates the maintenance of sets of rules. Another line of research distinct from autoepistemic logic and other nonmonotonic logics based on consistency uses model preference [ Shoham, 1987; Kraus et al. 1990 ] Shoham denes a general framework of preferential logics in which both nonmonotonicity and resolution of conAEicts between defaults are achieved using model preference. Kraus et al. 1990 ] use a framework similar to Shoham s for dening logics in which conAEicts are solved ....

Shoham, Y.: Nonmonotonic logics: meaning and utility. In D. McDermott, editor, Proceedings of the 10th International Joint Conference on Articial Intelligence, pages 388393, Milano, 1987.

.... a set of alternative, incompatible models for a single scenario, how can we select the most appropriate one Shoham answered this by proposing model preference semantics by which the set of models is partially ordered by means of some preference criterion appropriate to the intended application (Shoham 1987). In the Transition Calculus we adopt a preference criterion corresponding to our determination to minimise unexplained state changes. Our criterion therefore consists of enumerating the unexplained state changes in each model and selecting a model with the smallest number. The enumeration is ....

Shoham, Y.: 1987, Nonmonotonic logics: Meaning and utility, Proceedings IJCAI-87, pp. 388-- 392.

....the only situations that exist are those that result from a finite sequence of actions beginning at the initial situation. 5 Other Work The first set of solutions to the frame problem, which proposed preferring change that happened as late in time as possible, were by Lifschitz [Lif86] Shoham [Sho86a, Sho86b, Sho87b, Sho87a, Sho88b, Sho88a, SM88, Sho87c], and Kautz [Kau86, AK85] These solutions are now grouped under the heading of chronological minimization, a term suggested by Shoham. It is worthwhile noting that these solutions did not change the basic default, the preference was still to assume that change happened as few times as possible, ....

Y. Shoham. Nonmonotonic logics: meaning and utility. In Proc. Tenth International Joint Conference on Artificial Intelligence (IJCAI '87), San Mateo, CA., 1987. Morgan Kaufmann.

....with intervals. 6 B x;t ; where is a tautology (13) B x;t B x;t ( oe ) oe B x;t (14) B x;t oe B x;t B x;t (15) B x;t oe B x;t :B x;t (16) We also have the rules of inference modus ponens and generalization. 3. 2 Nonmonotonic Reasoning in This Framework It has been shown[6] that many nonmonotonic logics are reducible to logical systems that utilize special semantics to select specific desirable models for their theories. In general, there will be many models for any particular set of sentences of T I. Not only do models of T I assign truth values to temporal ....

Shoham, Y. (87), Nonmonotonic Logics: Meaning and Utility, Proceedings of the Seventh International Joint Conference on Artificial Intelligence, Milan, Italy, 1987.

....of naturals with as the usual less than or equal relation. By abuse of notation, we define: M[ power] x) x 2 ; M 0 [ power] x) x 3 : Of course, M[ power] x) M 0 [ power] x) and it is easy to establish M (power; M 0 . 5 Please refer to Lifschitz [Lif94] and Shoham [Sho87] for a general discussion and results on preferential models. 6 In this definition, ordering R is external to the theory, i.e. R is not a predicate defined in the theory. Finally, let us proceed to state that models of formula (1) are all and only those which are minimal w.r.t. F ;R) Z . ....

Y. Shoham. Nonmonotonic logics: meaning and utility. Proc. the of 10th IJCAI Conference, (1987) 388--393.

....restricted classes of models rather than all possible worlds. For example, Moore (1985) employs standard epistemic modal logics; Konolige (1985) permits one to use different incomplete sets of ordinary sound rules; Levesque (1984) employs situational models connected with relevance logic; and Shoham (1987) presents a version of circumscriptive entailment based on the concept of minimal models. Except for Shoham s, these theories of belief all agree on the essentially deductive nature of constructive beliefs. There is no requirement that either manifest or constructive beliefs be complete, but the ....

.... not presented in terms of rational choice, and their mechanization usually involves no decision theoretic calculations (see Section 8) But when closely examined, they are clearly based on rational responses to computational problems involving incomplete information (see (Doyle 1983) and (Shoham 1987)) Taking action requires information about the available actions, about their expected consequences, and about the utility of these consequences to the agent. Ordinarily, obtaining such information requires effort, it being costly to acquire the raw data and costly to analyze the data for the ....

Shoham, Y., 1987. Nonmonotonic logics: meaning and utility, Proceedings of the Tenth International Joint Conference on Artificial Intelligence, 388-393.

....which is inconsistent, and so must be false, contravening (iv) 2 Given these four intuitive properties are inconsistent, it is interesting to consider which property different systems have given up. i) is given up in circumscription [ McCarthy, 1986 ] in any minimal model solution [ Shoham, 1987 ] and systems which require membership in all extensions [ McDermott and Doyle, 1980 ] This is because they want the expressiveness that property (iii) gives, they need property (ii) by their very nature, and always reject having inconsistent extensions or reducing to no models. ii) is given up ....

....the system if the proportion of exceptions does not have measure zero. In particular this system does not seem appropriate to represent birds fly , as it is not true there are infinitesimally few birds that don t fly. His semantics means accepting the convention view of defaults (section 4. 3) Shoham [ 1987 ] rejects the one step default property in his discussion on the lottery paradox. However his discussion indicates that we would not want to write such defaults, but explicitly rejects the view of defaults as autoepistemic statements (section 4.3) Rather than indicating to the user that the ....

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Y. Shoham, "Nonmonotonic Logics: Meaning and Utility", Proc. IJCAI-87, pp. 388-393.

....most influential work can be seen as a reified approach [80, 4, 63, 24] although it is not completely clear what the underlying logic is because, although their formulate their logics as a many sorted first order one, no one provides a special formal semantics for their temporal features. Shoham [103] is an exception. He presents a formally defined reified logic and sets out that it is more general than McDermott and Allen systems. It is interesting to have a look in detail at Shoham s formalization. Let s see the first order case: Syntactically it has a vocabulary similar to a Temporal ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. IJCAI'87, pages 388--393, 1987.

....of nonmonotonic reasoning based on the use of a modal operator have been proposed in [13, 15] The knowledge of an agent is characterized in terms of a fixed point equation that expresses its introspective capabilities. A different approach for defining nonmonotonic modal logics was taken in [3, 22, 7], where the knowledge of the agent is characterized on a semantic ground, following the idea of selecting those models in which knowledge is minimal. Recently, there have been a number of attempts to reconcile the fixed point and semantic characterizations of modal nonmonotonic logics. In order to ....

.... the minimization of objective facts, or, in other terms, to study the family of ground logics, for which we find an appropriate semantic characterization, that has been advocated in [21] In particular, the characterization we present is an instance of the preference semantics introduced by Shoham [22], where the preference criterion is given by a partial ordering over possible world models. We show the correspondence between such semantic characterization 1 A more recent version of this work [8] contains a technical difference which makes the resulting logic a logic of minimal belief , that ....

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Y. Shoham. Nonmonotonic logics: meaning and utility. In Proc. of the 10th Int. Joint Conf. on Artificial Intelligence IJCAI-87, Milan, 1987.

....we can consider an S5 model as a set of propositional interpretations, i.e. a universal S5 model [20, Theorem 7.52] M 0 , if M 0 contains all the interpretations of M then M 0 6j= Sigma. Such a semantics gives to the modal operator K of the logic S5G a minimal knowledge interpretation [12, 27], which is very similar to the minimal belief interpretation of the MBNF operator B. Indeed, it is easy to see that, for positive subjective MBNF theories, there is a one to one correspondence between MBNF models of a theory Sigma and S5G models of the theory Sigma K , which is the theory ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pp. 388--392, 1987.

....able to provide a partial ordering relation on Kripke models. Definition 2.3 Given two Kripke models M 1 , M 2 , M 2 G M 1 if there exists a Kripke model M such that M 2 oe G M fi M 1 . Minimal models are characterized using the G ordering, as a special case of Shoham s preference semantics [Sho87] Definition 2.4 Given a normal modal logic S characterized by the class of Kripke models C, a model M 2 C is a ground C minimal model for I if M j= I and for every model M 0 2 C such that M 0 j= I, M 0 6 G M. Finally, we state the equivalence between the fix point and semantic ....

Y. Shoham. Nonmonotonic logics: meaning and utility. In Proc. of IJCAI87, pages 388--392, 1987.

....in a more abstract way, and look at the space of all possible default semantics. We can classify them by means of the valid deduction rules (and other properties, such as the preservation of consistency) There is a rich literature on nonmonotonic consequence relations (e.g. Gabbay, 1985; Shoham, 1987; Makinson, 1989; Kraus et al. 1990; Brass, 1990; Dix, 1991; Makinson, 1992 ] but our way of deriving a default semantics from given properties seems to be novel. Of course, the soundness of certain deduction rules has been proved or disproved for the known default semantics. The aim of this ....

Yoav Shoham. Nonmonotonic logics: Meaning and utility. In Proc. 10th International Joint Conference on Artificial Intelligence (IJCAI), pages 388--393, Milan, 1987. Our papers are available from the anonymous ftp-server "wega.informatik.uni-hannover.de" (130.75.26.1).

.... the modality K coincides with the epistemic operator of the modal logic defined by Halpern and Moses in [ Halpern Moses, 1985 ] also known as ground nonmonotonic modal logic S5G [ Donini, Nardi, Rosati, 1997b ] which modifies modal logic S5 through a very intuitive preference semantics [ Shoham, 1987 ] consider only the models of the knowledge base (i.e. the epistemic states of the agent modeled) in which the knowledge on the objective facts is minimal (i.e. the ignorance of the agent is maximal) The operator not can be considered as a generalization of the negation as failure operator ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pp. 388--392, 1987.

....intuitive motivation: in fact, it corresponds to discarding the reasoning based on epistemic assumptions, which, for example, would enable the agent to conclude that something is true in the world, by assuming to know it. A different approach for defining nonmonotonic modal logics was taken in [10, 30, 14], where the knowledge of the agent is characterized on a semantic basis, by means of a preference criterion among the models of the agent s initial knowledge. Many of such criteria follow the idea of selecting those models in which knowledge is minimal. Recently, there have been a number of ....

....from the semantical, computational and epistemological viewpoint. With respect to the first issue, we present an appropriate semantic characterization for ground logics, that has been advocated in [29] In particular, our proposal is an instance of the preference semantics introduced by Shoham [30], where the preference criterion is given by a partial ordering over possible world models and generalizes the idea of minimal knowledge as proposed in [10, 30, 14] We show the correspondence between such semantic characterization and the fix point definition of ground logics for a subclass of ....

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Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), pages 388--392, 1987.

....circumscription, have proposed particular mechanisms for default reasoning, and might therefore be considered quite specialised. However, there has also been work on more general approaches which attempt to analyse in broader terms what default reasoning involves. An early attempt to do this was Shoham s (1987) proposal that all non monotonic systems could be characterised in terms of the preference order over their models. A more proof theoretic strand of this research has investigated the formalisation of the underlying requirements for any non monotonic consequence relation. Perhaps the most ....

Shoham, Y. 1987. Nonmonotonic logics: meaning and utility. In Proceedings of the 10th International Joint Conference on Artificial Intelligence, 388--393.

....F . This correspondence allows us to give a maximal model semantics to default logic. The presentation here follows that in [Etherington, 1987a] which builds on the work in [Etherington, 1987c; Lukaszewicz, 1985] Sets of models are compared rather than individual models as in other frameworks [Shoham, 1987]. Sets of models are needed as we need to capture derivability, which is needed for both ensuring that preconditions are met, and for ensuring that justifications are consistent. The maximal model semantics can be defined as follows. Definition 4.2 If M 1 and M 2 are sets of models of F , we say ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. 10th International Joint Conf. on Artificial Intelligence (IJCAI-87), pages 388--393, Milan, August 1987.

....is more than just an interpretation: it provides a justification for the formal structures of the various nonmonotonic logics. The original theories provided precise formal concepts, but motivated explanations of why these concepts were interesting appeared only later, when Doyle [6, 9] Shoham [55], and others [26, 28] justified default rules by an appeal to decision theoretic rationality, saying that an agent should adopt a default conclusion or default rule if the expected inferential utility of holding it exceeds that of not holding it. Default rules and other assumptionmaking mechanisms ....

Shoham, Y. Nonmonotonic logics: Meaning and utility. in: Proceedings of the Tenth International Joint Conference on Artificial Intelligence, pages 388--393, 1987.

....classical entailment is defined by a model theoretic presentation, we now have to focus on such logics in which nonmonotonic entailment, too, has a semantical background. A large and natural such class is comprised of those logics in which nonmonotonic entailment has a preferential model semantics (Shoham 1987). We here generalize the notion of preferential models in one aspect, for which we need the following preparatory definition. Definition 4.5 Let L be a logic with a modeltheoretic presentation, S a vocabulary, and S the class of S structures. We say that S is locally ordered iff on every subset ....

Shoham, Y. (1987), Nonmonotonic logics: Meaning and utility, in `Proceedings of IJCAI-87'.

.... specification can be written either at the level of the possible alternative sets of beliefs that are the intended outcomes, or at the level of reasoning patterns to construct these outcomes (or both) The first type of specifications at least covers approaches such as preferential semantics (cf. [Sho87]) and the notion of Sexpansions for modal nonmonotonic logics (cf. MT93] The second type at least covers approaches like default logic (cf. Rei80] The general specification framework (and its semantics) introduced here provides a unifying perspective on these and other well known approaches. ....

....that an information state is closed under propositional consequence: the syntactical form in which the initial facts are given, is not important. Level 1 semantically consists of descriptions of nonmonotonic reasoning using belief state frames. As an example we consider preferential semantics (cf. [Sho87]) Let a preference relation on Mod be given. A belief state operator (with single belief states) can be defined in the following manner: for each X L (X) m Mod m is minimal in Mod(X) Preferential semantics essentially provides a level 1 description, abstracting from lower ....

Shoham, Y.: Nonmonotonic Logics: Meaning and Utility, In: J. McDermott (ed.), Proc. 10th International Joint Conference on Artificial Intelligence, IJCAI-87, Morgan Kaufmann, 1987, pp. 388-393

....extended to provide a preference semantics for ground logics [20] A byproduct of such semantic characterizations is the possibility of designing semantic tableaux calculi for NMMLs, which are the subject of this paper. The formalisation of nonmonotonic reasoning based on a preference semantics [30, 26] embodies the idea that not every model is to be taken into consideration, and attention must be restricted to those models that are preferred according to a preference relation. This issue has been addressed in [24] for circumscription, where in building a tableau for CIRC( Sigma) j= the ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pages 388--392, 1987.

....of populations with certain properties) does affect the defaults we make. In this paper we consider a formulation of defaults that takes probability and utility into consideration. 1. 2 The Proposal Other people have observed that utilities have something to do with default reasoning [ Shoham, 1987; Loui, 1990; Doyle, 1989; Kadie, 1988 ] In this paper we take this relationship seriously and treat defaults as decision theory summaries. A default e A a means that a is the best decision out of those decisions in A if all you know is e. Note that the conclusion of a default is an action, and ....

....default reasoning. The group decision making and the individual decision making used in this paper are not incompatible (unless we want to claim they are the same [ Doyle and Wellman, 1989 ] and so these approaches should be seen as complementary to the approach propounded here. 6. 2 Shoham Shoham [ 1987 ] has argued that we should take probabilities and utilities into account when considering defaults. Here we take this suggestion seriously and consider the normative theory of decision making as a starting point. He instead develops a general framework of nonmonotonic reasoning based on ordering ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. 10th International Joint Conf. on Artificial Intelligence, pages 388--393, Milan, August 1987.

....default rule : p q . It turns out that, when restricting to K formulas, MKNF corresponds to the modal logic of minimal knowledge due to Halpern and Moses [7] also known as ground nonmonotonic modal logic S5G [22] The semantics of K formulas can be given by simplifying Definition 1 as follows [21]: M is a model for Sigma 2 LK iff M j= Sigma and, for each M 0 , if M 0 j= Sigma then M 0 6oe M . In other words, when Sigma 2 LK , a cluster M satisfying Sigma is compared with all other clusters satisfying Sigma, while in the case Sigma 2 LM the cluster M is only compared with ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pp. 388--392, 1987.

....we conclude their conjunction, which is inconsistent, contravening (iv) 2 Given that these five intuitive properties are inconsistent, it is interesting to consider which property different systems have given up. i) Conditioning is given up in circumscription [26] in any minimal model solution [43] and in systems which require membership in all extensions [27] This is because they want the expressiveness that property (iii) gives, they need property (ii) by their very nature, and always reject having inconsistent extensions or reducing to no models. This means that they cannot guarantee ....

Y. Shoham, "Nonmonotonic Logics: Meaning and Utility", Proc. IJCAI87, pp. 388-393, 1987.

....reasoning, like autoepistemic logic, default logic, circumscription, and several McDermott and Doyle s logics. Also, reasoning with only knowing is easier (unless the polynomial hierarchy collapses) than reasoning in nonmonotonic modal formalisms based on the minimal knowledge paradigm [26], like Halpern and Moses s logic of minimal epistemic states [3] Lifschitz s logic MBNF [23] and the moderately grounded version of autoepistemic logic [4] This last observation can be rephrased as follows: minimal knowledge is harder than only knowing. In the following, we first briefly ....

....knowledge paradigm, e.g. 6,9,16,17,8,27,24] Among them, the first attempt in this direction is due to Halpern and Moses [6] and is the most similar to the notion of only knowing. Informally, Halpern and Moses apply minimal knowledge to modal logic S5: thus, they define a preference semantics [26] over S5, by considering as intended models of a modal theory Sigma only those S5 models satisfying Sigma in which the set of possible worlds is maximized. Hence, in this case the notion of maximization lies at the semantic level. Recently, it has been proven [3] that reasoning in Halpern and ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI-87), pages 388--392, 1987.

.... of the early works on default and defeasible reasoning (e.g. McCarthy, 1980 ] In particular, several works use expected utility consideration in evaluation of heuristic rules (e.g. Langlotz et al. 1986 ] More recently, decision theoretic foundations for defaults were advocated by Shoham (1987) and Doyle (1989) Doyle provides a formal analysis of Pascal s wager and shows how an assumption (the existence of God) can be justified in terms of utility. Finally, Poole (1992) examined a concrete notion of defaults that are grounded in terms of decision theory. Unlike previous works (with ....

Y. Shoham. Nonmonotonic logics: meaning and utility. In Proc. 10th International Joint Conference on Artificial Intelligence (IJCAI '87), pp. 388--393. 1987.

....is explanations that we know how to compute. The best way to see point 2 is in terms of arguments. The set D is a set of arguments for g for which there is no counter argument which simultaneously argues against each element of D (see [30] Point 3 is a semantic notion in terms of minimal models [45], that is related to the circumscriptive [23, 22] notion of minimal models (see section 4.2.1 below) Proof: 1 ) 2. Let A be the set of all explanations of g. If C is an explanation of : W C i 2A C i , then C can be extended to an extension E, in which g does not appear (as F [ C implies the ....

....can choose. Game theory allows for multiple moves by different agents and by nature. ffl Utility and values play an integral part in decision and game theory. They are not part of nonmonotonic formalisms, although it has been admitted that values do play a part in what assumptions should be made [45, 8]. Utilities have not been explicit, and maybe they need to be so that they can be reasoned about and not compiled into a set of assumptions. ffl What information is available to agents when making a decision is also important (as we do not always have perfect information ) This plays an ....

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Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. 10th International Joint Conf. on Artificial Intelligence, pages 388--393, Milan, August 1987.

....q. It turns out that, when restricting to K formulas, MKNF corresponds to the modal logic of minimal knowledge due to Halpern and Moses (Halpern and Moses 1985) also known as ground nonmonotonic modal logic S5G . The semantics of K formulas can be given by simplifying Definition 1 as follows (Shoham 1987): M is a model for Sigma 2 LK iff M j= Sigma and, for each M 0 , if M 0 j= Sigma then M 0 6oe M . In other words, when Sigma 2 LK , a cluster M satisfying Sigma is compared with all other clusters satisfying Sigma, while in the case Sigma 2 LM the cluster M is only compared with ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pp. 388--392, 1987.

....or in [12] relying on a problem space and a general measure on this space) but to give a specific (and hopefully useful) meaning to such constraints leading to efficient solving techniques. Non standard logics are manifold that allows the expression of probabilities [22] or preferences [27]. In particular, Zadeh s possibility theory [28] has already been successfully used for modeling uncertainty and preferences in the frame of propositional and first order logic by Dubois, Prade and Lang leading to the so called possibilistic logic [17] One of the desirable feature of ....

Shoham (Y.). -- Nonmonotonic logics : Meaning and utility. In : Int. Joint Conf. on AI, pp. 388--393.

....These choices are only made when a contradiction is derived. As long as no contradiction is derived, the knowledge is assumed to be consistent. This makes it possible to define an executable deduction process for the preference logic. For the logic a semantics based on the ideas of Y. Shoham [14, 15], is defined. It turns out that the semantics for the logic is a preferential semantics according to the definition S. Kraus, D. Lehmann and M. Magidor [9] Therefore the logic is a logic of system P and possesses all the properties of an ideal non monotonic logic. 1 Introduction In many ....

....in O(n) steps where n is the number of in justifications. begin B i = repeat P ) 2 J i ; J i : J i Gamma fP ) g; if P Delta i then B i : B i [ f g; until J i = return B i ; end. 6 The semantics for the logic The semantics of the logic is based on the ideas of Y. Shoham [14, 15]. In [14, 15] Shoham argues that the difference between monotonic logic and non monotonic logic is a difference in the definition of the entailment relation. In a monotonic logic a proposition is entailed by the premisses if it is true in every model for the premisses. In a non monotonic logic, ....

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Shoham, Y., Non-monotonic logic: meaning and utility, IJCAI-87 (1987) 388393.

....NP hard in the propositional case and is not even semi decidable in the first order case [27] One response is to attempt to find tractable subsets of nonmonotonic logics. This paper suggests instead a model based approach. 2 A mathematical theory Building on the work of McCarthy [36] and Shoham [45, 46], it is possible to give a general model theoretic framework for nonmonotonic logics, which also provides the basis of a mathematical theory of pragmatic reasoning. We begin with the definition of semantic logics. Definition 2.1 A semantic model for a language L is a pair M = I, M ) ....

....such as conjunction of consequences; # # .PM # and # # .PM # do not imply # # .PM ###. Consequently it seems better to read # # .PM # as # suggests # . In [9] many well known nonmonotonic logics (such as Default Logic, Autoepistemic Logic, Circumscription, Preference Logics [45], Cumulative Logics [30] and Negation as Failure [16] are shown to be pragmatic logics; indeed, once a nonmonotonic logic has a model theory, its inclusion is straightforward. Pragmatic logics thus provide a unifying model theoretic framework in which to study nonmonotonic logics. More ....

Y. Shoham (1987) Nonmonotonic logics : meaning and utility, Proceedings of the 10th International Joint Conference on Artificial Intelligence, Milan, Italy, J. McDermott (ed.), Morgan Kaufmann, San Mateo, California, 388-393.

.... logics, and, more generally, that McDermott and Doyle s characterization can be considered a very powerful schema for defining nonmonotonic modal logics [14, 25, 24] On the other hand, several researchers have proposed various notions of nonmonotonic modal logics based on a preference semantics [26] on models of a monotonic modal logic. Among these approaches, the logic of minimal knowledge states, due to Halpern and Moses [7] is based on a simple and natural preference semantics on modal logic S5 [26, 11] which realizes the intuitive principle of minimization of the knowledge of the ....

....proposed various notions of nonmonotonic modal logics based on a preference semantics [26] on models of a monotonic modal logic. Among these approaches, the logic of minimal knowledge states, due to Halpern and Moses [7] is based on a simple and natural preference semantics on modal logic S5 [26, 11], which realizes the intuitive principle of minimization of the knowledge of the agent modeled. Such a logic, initially proposed for modeling knowledge and ignorance of processes in a distributed computer system, constitutes the basis of several nonmonotonic modal formalisms proposed in the ....

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Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pp. 388--392, 1987.

....to provide a preference semantics for ground logics [20] A byproduct of such semantic characterizations is the possibility of designing semantic tableaux calculi for NMMLs, which constitute the subject of this paper. The formalisation of nonmonotonic reasoning based on a preference semantics [31, 27] embodies the idea that not every model is to be taken into consideration, and attention must be restricted to those models that are preferred according to a preference relation. This issue has been addressed in [24] for circumscription, where in building a tableau for CIRC( Sigma) j= the ....

Y. Shoham. Nonmonotonic logics: Meaning and utility. In Proc. of IJCAI-87, pages 388--392, 1987.

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Shoham, Y.: Nonmonotonic Logics: Meaning and Utility, In: J. McDermott (ed.), Proc. 10th International Joint Conference on Artificial Intelligence, IJCAI-87, Morgan Kaufmann, 1987, pp. 388-393

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Shoham, Y. 1987. Nonmonotonic logics: Meaning and utility. In Proc. of the 10th Int. Joint Conf. on Artificial Intelligence (IJCAI'87), 388--392.

No context found.

Y. Shoham. Nonmonotonic logics: meaning and utility. In: Proc. 10th International Joint Conference on Artificial Intelligence, Morgan Kaufmann, pp. 388--393, 1987.

No context found.

Y. Shoham. Nonmonotonic logics: meaning and utility. In: Proceedings of the 10th International Joint Conference on Artificial Intelligence, Morgan Kaufmann, pp. 388--393, 1987.

No context found.

Yoav Shoham. Nonmonotonic logic: meaning and utility. In Proc. of AAAI-87, pages 388--393, 1987. 66

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Shoham, Yoav, 1987. "Nonmonotonic Logics: Meaning and Utility", Proceedings, International Joint Conference on Artificial Intelligence, pp. 388--393. Milano, Italy, August 1987.

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Y. Shoham, Nonmonotonic Logics: Meaning and Utility, In: J. McDermott (ed.), Proc. 10th International Joint Conference on Artificial Intelligence, IJCAI-87, Morgan Kaufmann, 1987, pp.388-393

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