A.C. Kakas and P. Mancarella. Generalised Stable Models: a Semantics for Abduction. In Proc. 9th European Conference on AI, ECAI90, Stockolm, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... has been proposed as a reasoning paradigm in AI for fault diagnosis [4] natural language understanding [4] default reasoning [15] 39] In the context of logic programming, abductive procedures have been used for planning [14] 48] 35, 34] knowledge assimilation and belief revision [23], 21] database updating [22] 11] showed the role of an abductive system for forms of reasoning, di erent from planning, in the context of temporal domains with uncertainty. The term abduction was introduced by the logician and philosopher C.S. Pierce (1839 1914) 38] who de ned it as the ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Arti cial Intelligence. John Wiley and sons, 1990.

....as refutation mode , the proof relies on demonstrating both the soundness and completeness of the Prolog abductive computation w.r.t. the classical logic description of abduction (at least in the context of the EC axiomatisation) described here. The proof of completeness builds on the work in [13] on a generalised stable model semantics for abduction, and is valid for a well defined class of deterministic EC domain descriptions. 3 A Case Study In this section we describe, via an example, an application of our approach to analysing Software Cost Reduction (SCR) specifications. We show how ....

Kakas, A. C, and Mancarella, P. (1990). Generalised Stable Models: A Semantics for Abduction. ECAI'90, Stockholm, pages 385-391.

....for the problem would be to consider 3 valued completion semantics ( 9] SLDNFA is still correct wrt to these semantics and for each , P is consistent. Another issue to be investigated is the soundness of SLDNFA wrt other more ne grained semantics such as the Generalised Stable Models ([12]) A completeness result on SLDNFA has been proven with respect to the completion semantics de ned for abductive normal programs in [4] The de nition is an extension of the de nition for non abductive programs. De nition 3.5 Let P be a normal abductive program based on some language L. The ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In proc. of ECAI-90, 1990.

....atoms exists such that M is a model of the logic program P [ M j= F for each F 2 T 7 Also this de nition is parametric in the choice of the logic programming semantics. All main logic programming semantics have been extended in this way (generalised completion [4] generalised stable [17] and generalised well founded semantics [33] 6] On the epistemological level, the obvious problem with these semantics is that they inherit the ambiguities and epistemological confusion of logic programming. For example, in the generalised completion semantics de ned in [4] models of an ....

....and epistemological confusion of logic programming. For example, in the generalised completion semantics de ned in [4] models of an abductive program represent possible worlds; negation is interpreted as classical negation. On the other hand, in the generalised stable semantics de ned in [17], models inherit the interpretation as atom belief sets of stable semantics; negation is interpreted as a modal operator. However, the classical embeddings of LP into AEL and DL cannot be simply extended to ALP frameworks. Another problem with ALP is the blurred relationship to classical logic. An ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Articial Intelligence. John Wiley and sons, 1990.

....in AI is widely accepted. Abduction has been used for fault diagnosis [6] natural language understanding [6] default reasoning [22] 50] In the context of logic programming, abductive procedures have been used for planning [21] 52] 46, 44] knowledge assimilation and belief revision [32], 30] database updating [31] 18] showed the role of an abductive system for forms of reasoning, different from planning, in the context of temporal domains with uncertainty. In [15, 17] the role of abductive logic programming for representing uncertainty in a logic programming formalism and ....

....completion semantics was proposed in [14] and [11] Like most semantics for abductive logic programs, 3 valued completion semantics assigns a 2 valued interpretation to abducible predicates. This is also the case in the 2 valued completion semantics [8] the 2 valued generalised stable semantics [32], and the 3 valued extended well founded semantics [49] The reason for this is explained in [11] and can be traced back to a well known argument formulated by Moore in [47] He argues that reasoning by 2 cases (i.e. something is either true or false) is crucial for reasoning 7 on uncertainty, ....

[Article contains additional citation context not shown here]

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....jInitially(t)j = 0 jHolds(t; s)j = 2 Theta jsj Result 1 jNoninertial(t; a; s)j = 2 Theta jsj Result 2 One easily verifies that j:j is a level mapping. 2 Several types of semantics have been defined for open logic programs: 2 valued completion semantics [3] generalised stable semantics [20], the generalised well founded semantics [28] 3 valued completion semantics and 3 valued (direct) partial) justification semantics with FEQ [7] Due to the fact that D is acyclic and in each clause of PD , the variables of the body occur in the head, all these semantics coincide in the (weak) ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....constraints. 1] proves that the resulting program is acyclic. The same holds for D 0 , and in fact for all transformed domain descriptions: Proposition 3.1 The translation D of any domain description D is acyclic. Several types of semantics have been defined for incomplete programs [3] [14], 19] 7] Due to the fact that D is acyclic and in each clause of PD , the variables of the body occur in the head, all semantics coincide in the (weak) sense that the set of all ground atoms implied by D under any of the semantics is identical. This extension of results of [1] is proven ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

.... systems [23] 22] In [7, 8] we proved the soundness of the procedure with respect to Completion semantics, in the sense that for any query Q and generated solution Delta: P Delta j= Q This implies the soundness of the procedure with respect to the Generalised Stable Model semantics of [14]: a generated solution can be extended in a natural way to a generalised stable model of the abductive program. As a completeness result we proved that the procedure generates all minimal solutions when the computation tree is finite. Related to our work, 2] also indicates a relationship between ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....and integrity constraints. Abducibles are atoms that can be added to programs, provided their addition does not violate the integrity constraints. Various forms of ALP have been presented in the literature (see [6] for a survey) Among those, the form of ALP presented by Kakas and Mancarella [8, 7] has played an important role in the development of the eld. Kakas and Mancarella propose both a semantics for ALP [8] by generalising the stable model semantics for NLP, and a proof procedure [7] by generalising the abductive proof procedure for NLP by Eshghi and Kowalski [5] However, the ....

....the integrity constraints. Various forms of ALP have been presented in the literature (see [6] for a survey) Among those, the form of ALP presented by Kakas and Mancarella [8, 7] has played an important role in the development of the eld. Kakas and Mancarella propose both a semantics for ALP [8], by generalising the stable model semantics for NLP, and a proof procedure [7] by generalising the abductive proof procedure for NLP by Eshghi and Kowalski [5] However, the Kakas Mancarella (KM) procedure is not sound with respect to the generalised stable model semantics, in the same way as ....

[Article contains additional citation context not shown here]

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In L. Carlucci Aiello, editor, Proc. ECAI, pages 385-391, Stockolm, 1990. Pitman.

.... has been proposed as a reasoning paradigm in AI for fault diagnosis [4] natural language understanding [4] default reasoning [14] 34] In the context of logic programming, abductive procedures have been used for planning [13] 43] 31, 29] knowledge assimilation and belief revision [21], 19] database updating [20] 11] showed the role of an abductive system for forms of reasoning, different from planning, in the context of temporal domains with uncertainty. The term abduction was introduced by the logician and philosopher C.S. Pierce (1839 1914) 33] who defined it as the ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence. John Wiley and sons, 1990.

....approaches to diagnosis, and so, for generality, we present a methodology that transforms a diagnostic problem of [3] into an extended logic program and solve it with contradiction removal. Another unifying approach to diagnosis with logic programming [23] uses Generalised Stable Models [11]. They present criticisms of Console and Torasso s approach which do not carry over to our representation, ours having the advantage of a more expressive language: explicit negation as well as negation as failure. We also set forth a method to debug pure Prolog programs, showing that declarative ....

....i.e. the diagnoses. The unifying approach of abductive and consistency based diagnosis presented by these authors enables us to represent easily and solve a major class of diagnostic problems using twovalued contradiction removal. Similar work has been done by [23] using Generalised Stable Models [11]. We start by making a short description of a diagnostic problem as defined in [3, 5] A DP is a triple consisting of a system description, inputs and observations. The system is modelled by a Horn theory describing the devices, their behaviours and relationships. In this diagnosis setting, each ....

A. C. Kakas and P. Mancarella. Generalised stable models: A semantics for abduction. In Proc. ECAI'90, pages 401--405, 1990.

....[9] showing how debugging can be envisaged as contradiction removal. Thus, exactly the same technique can be employed to first debug the blueprint specification of an artifact, and used next to perform diagnoses with the debugged specification. Because [16] relies on Generalised Stable Models [7] to define diagnoses, they are at odds to produce an algorithm to compute minimal ones, as they themselves acknowledge (p. 520) Instead of requiring a new semantics we view diagnoses as an iterative program update process. Our use of normal logic programs extends that of Horn programs made by ....

....i.e. the diagnoses. The unifying approach of abductive and consistency based diagnosis presented by these authors enables us to represent easily, and solve, a major class of diagnostic problems using contradiction removal. Similar work has been done by [16] using Generalised Stable Models [7]. We start by making a short description of a diagnostic problem as defined in [1, 2] A DP is a triple consisting of a system description, inputs and observations. The system is modeled by a Horn theory describing the devices, their behaviours and relationships. In this diagnosis setting, each ....

A. C. Kakas and P. Mancarella. Generalised stable models: A semantics for abduction. In Proc. ECAI'90, pages 401--405, 1990.

....more effective. It has been argued ( 5] that abductive inference and its parallel realisation should be one of the future research themes in parallel logic programming. The development of an abductive framework in logic programming has been proposed in [4] and further developed, among others, in [7,8]. An abductive logic program is a triple P,A,I where P is a general logic program, A is a set of abducible atoms and I a set of constraints. For simplicity a number of restrictions are usually imposed: there are no rules for abducible atoms, integrity constraints are compiled into denials with ....

....the extent to which the system resorts to abduction in breaking the deadlock. This parameter states the conditions under which abductive hypotheses can be generated. The simplest form of such integrity constraints is negation combined with the restriction that hypotheses should be variable free ([7,8]) As an example, consider the following query. abductive parlog(Goal,Constraints) Goal= circuit(S,B1,B2,B3,W1,W2,W3,W4,W5,W6,off,on,off) print( S,B1,B2,B3] Constraints= not( S=empty,B1=on) not( S=empty,B2=on) not( S=empty,B3=on) The user has imposed the constraint that if at least ....

A. C. Kakas and P. Mancarella (1990), `Generalised Stable Models: a Semantics for Abduction', Proc. 9th European Conference on Artificial Intelligence, Stockholm, Sweden, pp. 385-391. Abductive Behaviour of Concurrent Logic Programs --- 11 ---

....formalism. In fact we notice that recently added constructs to DLs, like reflexive transitive closure of roles, map to more expressive subsets of OLP for which stronger LP semantics than the completion (for example the justification semantics of [10] or the generalized stable model semantics of [16]) are appropriate. In sections 2 and 3, we describe syntax and semantics of OLP and Description Logics, respectively. In the fourth section we provide a mapping from DL theories into open logic programs and indicate to which sublanguages of OLP different DLs correspond. Section 5 discusses ....

A. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....with comp(P ) A trivial example is the incomplete program with normal clause p : p and undefined predicate r. The goal r is solved by Delta = frg, but comp(P Delta) is inconsistent. The same example also shows that SLDNFA is in general not sound wrt the generalised stable semantics [21]: the set frg cannot be completed to a generalised stable model of P . The example shows that to build a sound abductive procedure for 2 valued completion semantics or generalised stable semantics, consistency checking is necessary. A sound abductive procedure has been developed for generalised ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....the use of other computational paradigms such as deduction and satisfiability checking on an equal basis as abduction. Second, the role of the formal model semantics is different in ALP and OLP. In ALP, a model semantics is meant as a specification of what abductive solutions must be computed [3] [14] [22] In contrast, we look at model semantics as a formalisation of the declarative and descriptive meaning of an OLP FOL theory. Third, the role of the FOL component in ALP and OLP seems different. In [13] a FOL formula is interpreted as an integrity constraint. The role of an integrity ....

....paper, one interesting advantage of using the 3 valued completion semantics is that it is the weakest semantics known for the (O)LP formalism. In [4] the following theorem is proven: Theorem 3. 2 If M is a model of P D wrt (2 valued completion semantics [2] 3] generalised stable semantics [14]) generalised well founded semantics [22] justification semantics [5] then M is a model of P D wrt 3 valued completion semantics. As a consequence, the 3 valued completion semantics induces the weakest entailment relation j= if an open theory entails F according to the 3 valued completion ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....Here we continue to use this terminology. With respect to the above aims, we face a serious problem here, namely the lack of a declarative semantics for the formalism. In the past many model semantics have been defined for abductive logic programming, for example the generalised stable semantics [13], the completion semantics for abductive logic programs [2] and the extended well founded semantics [22] In [6] we proposed the justification semantics. It is important to realise that all except the justification semantics were introduced from the nonmonotonic perspective on logic programming. ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....jInitially(t)j = 0 jHolds(t; s)j = 2 Theta jsj Result 1 jNoninertial(t; a; s)j = 2 Theta jsj Result 2 One easily verifies that j:j is a level mapping. 2 Several types of semantics have been defined for open programs: 2 valued completion semantics [3] generalised stable semantics [20], the generalised well founded semantics [27] 3 valued completion semantics and 3 valued (direct) partial) justification semantics with FEQ[7] Due to the fact that D is acyclic and in each clause of PD , the variables of the body occur in the head, all these semantics coincide in the (weak) ....

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In Proc. of the European Conference on Artificial Intelligence, 1990.

....has been studied in [10, 11] within an abductive logic programming framework whose semantics was defined by a suitable extension of the completion semantics of LP. In parallel to these studies of abduction as an inferential method, Eshghi and Kowalski [29] and later Kakas and Mancarella in [52, 54] and Dung in [25] used abduction as a semantical device to describe the non monotonic semantics of Logic Programming (in a way analogous to Poole in [81] In [18, 14] abductive logic programming was investigated from a knowledge representation point of view and its suitability for representing ....

....same way as the query. The above definition aims to define the concept of an abductive solution for a query but does not define abductive logic programming as a logic in its own right as a pair of syntax and semantics. However, a notion of generalized model can be defined, originally proposed in [52], which suggests the following definition. Definition 2. M is a model of an abductive logic framework (P, A, IC) i# there exists a set # A such that M is a model of P # (according to some LPsemantics) and M is a classical model of IC, i.e. M IC. The entailment relation between abductive ....

[Article contains additional citation context not shown here]

A.C. Kakas and P. Mancarella. Generalised Stable Models: a Semantics for Abduction. In Proc. 9th European Conference on AI, ECAI90, Stockolm, 1990.

....diagnosis has been studied in [8, 9] within an abductive logic programming framework whose semantics was de ned by a suitable extension of the completion semantics of LP. In parallel to these studies of abduction as an inferential method, Eshghi and Kowalski [24] and later Kakas and Mancarella in [45, 47] and Dung in [20] used abduction as a semantical device to describe the non monotonic semantics of Logic Programming (in a way analogous to Poole in [70] In [13, 11] abductive logic programming was investigated from a knowledge representation point of view and its suitability for representing ....

....in most versions of ALP. The above de nition aims to de ne the concept of an abductive solution for a query but does not de ne abductive logic programming as a logic in its own right as a pair of syntax and semantics. However, a notion of generalized model can be de ned, originally proposed in [45], which suggests the following de nition. De nition 3.2 M is a model of an abductive logic framework (P; A; IC) i there exists a set A such that M is a model of P [ according to some LP semantics) and M is a classical model of IC, i.e. M j= IC. The entailment relation between abductive ....

[Article contains additional citation context not shown here]

A.C. Kakas and P. Mancarella. Generalised Stable Models: a Semantics for Abduction. In Proc. 9th European Conference on AI, ECAI90, Stockolm, 1990.

....and integrity constraints. Abducibles are atoms that can be added to programs, provided their addition does not violate the integrity constraints. Various forms of ALP have been presented in the literature (see [6] for a survey) Among those, the form of ALP presented by Kakas and Mancarella [8, 7] has played an important role in the development of the field. Kakas and Mancarella propose both a semantics for ALP [8] by generalising the stable model semantics for NLP, and a proof procedure [7] by generalising the abductive proof procedure for NLP by Eshghi and Kowalski [5] However, the ....

....the integrity constraints. Various forms of ALP have been presented in the literature (see [6] for a survey) Among those, the form of ALP presented by Kakas and Mancarella [8, 7] has played an important role in the development of the field. Kakas and Mancarella propose both a semantics for ALP [8], by generalising the stable model semantics for NLP, and a proof procedure [7] by generalising the abductive proof procedure for NLP by Eshghi and Kowalski [5] However, the Kakas Mancarella (KM) procedure is not sound with respect to the generalised stable model semantics, in the same way as ....

[Article contains additional citation context not shown here]

A.C. Kakas and P. Mancarella. Generalised stable models: a semantics for abduction. In L. Carlucci Aiello, editor, Proc. European Conference on Artificial Intelligence, pages 385--391, Stockolm, Sweden, 1990. Pitman.

....of Abductive Logic Programming (ALP) Many of the ideas however are applicable, more generally, to other frameworks of abduction or hypothetical reasoning. The framework of ALP that we will adopt was originally proposed by Eshghi and Kowalski ( 4,5] and developed further by Kakas and Mancarella ([12,13]) The operational semantics for sequential execution of abduction is well defined within this framework and has been used in building meta interpreters on top of Prolog systems. However, as in ordinary (deductive) logic programming, abductive inference mechanisms have several sources of ....

.... = G and P D satisfies the integrity constraints I where = is given by some chosen underlying semantics for logic programming, and ii) P D satisfies I under some notion of integrity constraint satisfaction. An example of this semantics for abduction is the generalised stable model semantics ([12]) In this D is an abductive explanation iff there exists a stable model M(D) of P D such that: i) M(D) G and ii) M(D) I where = denotes truth in the model M(D) For simplicity we assume the usual restrictions: there are no rules for abducible atoms, integrity constraints have been compiled ....

[Article contains additional citation context not shown here]

Kakas A. C. and Mancarella P., Generalised Stable Models: a Semantics for Abduction, 9th ECAI, Stockholm, 1990, pp. 385-391.

No context found.

Kakas, A. C., and Mancarella, P. (1990). Generalised Stable Models: a semantics for abduction. Proceedings of the European Conference on Artificial Intelligence (ECAI90), Stockolm, pp. 385-391, Pitman.

No context found.

Kakas, A., and Mancarella, P. (1990). Generalised Stable Models: a Semantics for Abduction. Proceedings of the 9th European Conference on Artificial Intelligence (ECAI'90), Stockolm, pp. 385-391.

No context found.

Kakas A. C. and Mancarella P., [1990]: Generalised Stable Models: a Semantics for Abduction, 9th European Conference on Artificial Intelligence, Stockholm, Sweden, pp. 385 - 391.

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