## Representing Knowledge in A-Prolog

Citations: | 60 - 1 self |

### BibTeX

@MISC{Gelfond_representingknowledge,

author = {Michael Gelfond},

title = {Representing Knowledge in A-Prolog},

year = {}

}

### OpenURL

### Abstract

In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of A-Prolog, can be used to represent various types of knowledge about the world. By way of example we demonstrate how the corresponding representations together with inference mechanisms associated with A-Prolog can be used to solve various programming tasks.

### Citations

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- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...ral language used in the informal descriptions of programming tasks faced by the programmer. In this paper we discuss A-Prolog { a language of logic programs under answer set (stable model) semantics =-=[27-=-],[28]. A-Prolog can be viewed as a purely declarative language with its roots in the syntax and semantics of standard Prolog [78], [19] and in the early work on nonmonotonic logic [66], [54]. It dier... |

1484 | Some philosophical problems from the standpoint of artificial intelligence
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(Show Context)
Citation Context ...he latter, known as the frame problem, is often reduced to the problem ofsnding a concise and accurate representation of the inertia axiom { a default which says that things normally stay as they are =-=[52]-=-. The search for such a representation substantially in uenced AI research during the last twenty years. An interesting account of history of this research together with some possible solutions can be... |

1423 |
A Logic for Default Reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...odel) semantics [27],[28]. A-Prolog can be viewed as a purely declarative language with its roots in the syntax and semantics of standard Prolog [78], [19] and in the early work on nonmonotonic logic =-=[66], [5-=-4]. It diers from many other knowledge representation languages by its ability to represent defaults, i.e. statements of the form \Elements of a class C normally satisfy property P ". One may lea... |

960 |
Negation as failure
- Clark
- 1978
(Show Context)
Citation Context ...uage of logic programs under answer set (stable model) semantics [27],[28]. A-Prolog can be viewed as a purely declarative language with its roots in the syntax and semantics of standard Prolog [78], =-=[19-=-] and in the early work on nonmonotonic logic [66], [54]. It diers from many other knowledge representation languages by its ability to represent defaults, i.e. statements of the form \Elements of a c... |

847 | Classical negation in logic programs and disjunctive databases
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...anguage used in the informal descriptions of programming tasks faced by the programmer. In this paper we discuss A-Prolog { a language of logic programs under answer set (stable model) semantics [27],=-=[28-=-]. A-Prolog can be viewed as a purely declarative language with its roots in the syntax and semantics of standard Prolog [78], [19] and in the early work on nonmonotonic logic [66], [54]. It diers fro... |

844 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...wn conditions which guarantee that the traditional SLDNF-resolution based goal-oriented methods of \classical" Prolog and its variants are sound with respect to various semantics of logic program=-=ming [79, 24, 38, -=-1]. All of these semantics are sound with respect to the semantics of A-Prolog, i.e. if a program is consistent under the answer set semantics and entails a literal l under one of these semantics th... |

709 | The semantics of predicate logic as a programming language - Emden, Kowalski - 1976 |

610 |
Towards a theory of declarative knowledge
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- 1988
(Show Context)
Citation Context ...hat for every rule r of 1. For any l 2 pos(r), jjljj jjhead(r)jj; 2. For any l 2 neg(r) jjljjsjjhead(r)jj. 14 This is a special case of the notion of stratied general logic program introduced in [2]. The results of that paper together with those from [26] imply that a stratied logic program has exactly one answer set. Forsnite stratied programs this can be easily obtained by induction on the n... |

381 | Bilattices and the semantics of logic programming
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- 1991
(Show Context)
Citation Context ...wn conditions which guarantee that the traditional SLDNF-resolution based goal-oriented methods of \classical" Prolog and its variants are sound with respect to various semantics of logic program=-=ming [79, 24, 38, -=-1]. All of these semantics are sound with respect to the semantics of A-Prolog, i.e. if a program is consistent under the answer set semantics and entails a literal l under one of these semantics th... |

381 | Representing actions and change by logic programs
- GELFOND, LIFSCHITZ
- 1993
(Show Context)
Citation Context ...owing corollary is useful for many application. Corollary 6.1 j= A h(l; t) i '(D) j= h(l; t). The systematic study of the relationship between entailment in action theories and in AProlog started in [=-=29-=-], where the authors formulated the problem and obtained some preliminary results. The above theorem is from [76] which contain some denitive results on the subject. Planning in A-Prolog Now we will s... |

368 | Logic for problem solving - Kowalski - 1979 |

331 | Programmes with Common Sense
- McCARTHY
- 1959
(Show Context)
Citation Context ...base representing this knowledge. The consequence relation of a language should be nonmonotonic, i.e. addition of new information to a knowledge base may invalidate some of the previous conclusions [=-=51]-=-. This property is especially important for representing common-sense knowledge about the world. In common-sense reasoning, additions to the agent's knowledge are frequent and inferences are often bas... |

326 | Logic programming with stable model semantics as a constraint programming paradigm
- Niemelä
- 1999
(Show Context)
Citation Context ...coveries (see for instance [37]) These engines are of course applicable only to programs withsnite Herbrand universes. Their eciency and power combined with so called answer sets programming paradigm =-=[56]-=-, [48] lead to the development of A-Prolog based solutions for various problems in several knowledge intensive domains [70, 59, 22]. This paper is an attempt to introduce the reader to some recent dev... |

289 |
ADL: exploring the middle ground between STRIPS and the situation calculus
- Pednault
- 1989
(Show Context)
Citation Context ...B. The corresponding action description contains a large number of static causal laws. It is interesting to notice that these laws, which are not available in more traditional planning languages like =-=[64-=-], played a very important role in our design. We are not sure that a concise, elaboration tolerant, and clear description of the eects of controller's actions could be achieved without their use. The... |

267 |
On closed world data bases
- Reiter
- 1987
(Show Context)
Citation Context ...(a); :q(b); p(b)g and hence its answer to a query q(b) would be no. Rule (2), read as \if there is no reason to believe that X satises q then it does not" is called the closed world assumption fo=-=r q [65]-=-. It guarantees that the reasoner's beliefs about q are complete, i.e. for any ground term t and every answer set S of the corresponding program, q(t) 2 S or :q(t) 2 S. The programs may have one, many... |

260 | Splitting a logic program
- Lifschitz, Turner
- 1994
(Show Context)
Citation Context ...methods of computation used in deductive databases. The newer methods (like that of [12]) combine both, bottom-up and top-down, approaches. A more detailed discussion of these matters can be found in =-=[41]-=-. In the last few years we witnessed the coming of age of inference engines aimed at computing answer sets (stable models) of programs of A-Prolog [57, 58, 18]. The algorithms implemented in these eng... |

258 | Smodels - an implementation of the stable model and well-founded semantics for normal logic programs
- Niemelä, Simons
- 1997
(Show Context)
Citation Context ...iled discussion of these matters can be found in [41]. In the last few years we witnessed the coming of age of inference engines aimed at computing answer sets (stable models) of programs of A-Prolog =-=[57, 58, 18-=-]. The algorithms implemented in these engines have much in common with more traditional satisability algorithms. The additional power comes from the use of techniques from deductive databases, good u... |

247 | Stable models and an alternative logic programming paradigm
- Marek, Truszczyński
- 1999
(Show Context)
Citation Context ...es (see for instance [37]) These engines are of course applicable only to programs withsnite Herbrand universes. Their eciency and power combined with so called answer sets programming paradigm [56], =-=[48]-=- lead to the development of A-Prolog based solutions for various problems in several knowledge intensive domains [70, 59, 22]. This paper is an attempt to introduce the reader to some recent developme... |

234 |
Negation in Logic Programming
- Kunen
- 1987
(Show Context)
Citation Context ...wn conditions which guarantee that the traditional SLDNF-resolution based goal-oriented methods of \classical" Prolog and its variants are sound with respect to various semantics of logic program=-=ming [79, 24, 38, -=-1]. All of these semantics are sound with respect to the semantics of A-Prolog, i.e. if a program is consistent under the answer set semantics and entails a literal l under one of these semantics th... |

223 | Logic programming and knowledge representation
- Baral, Gelfond
(Show Context)
Citation Context ...decided. Rules (r6) and (r7) can be viewed as a result of the application of the general methodology of representing defaults in A-Prolog. More detailed discussion of this methodology can be found in =-=[7]-=-. A more general approach which provides means for specifying priorities between defaults can be found in [33], [20]. Since we assume that in databases from C 0 a live person P has a complete record o... |

191 |
Autoepistemic logic
- Marek, Truszczyński
- 1991
(Show Context)
Citation Context ...g we will mean restrictions of A-Prolog and DA-Prolog to languages withsnite Herbrand universes. Theorem 5.1 1. The problem of deciding whether a program of FA-Prolog has an answer set is NP-complete =-=[4-=-7]. 2. A decision problem P can be solved by a uniform program of FA-Prolog i it is in the class NP [68] 3. A decision problem P can be solved by a uniform program of FDA-Prolog i it is in the complex... |

184 | Action languages
- Gelfond, Lifschitz
- 1998
(Show Context)
Citation Context ...rming actions and reasoning about their eects. Such domains are often called dynamic domains or dynamic systems. Our description of dynamic domains will be based on the formalism of action languages [=-=32]-=-. Such languages can be thought of as formal models of the part of the natural language that are used for describing the behavior of dynamic domains. A theory in an action language normally consists o... |

180 | Causal theories of action and change
- McCain, Turner
- 1997
(Show Context)
Citation Context ...e set E(a; ) of the \direct eects" of a with the set \ 0 of facts that are \preserved by inertia". The application of Cn(Z) adds the \indirect eects" to this union. The above denition=-= is from [49]-=- and is the product of a long investigation of the nature of causality. (See for instance, [42].) The following theorem (a version of the result from [76]) shows the remarkable relationship between ca... |

179 |
Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia
- Shanahan
- 1997
(Show Context)
Citation Context ...ch for such a representation substantially in uenced AI research during the last twenty years. An interesting account of history of this research together with some possible solutions can be found in =-=[67-=-]. In this paper we limit our attention to an action description language B [32] which signature consist of two disjoint, non-empty sets of symbols: the set F ofsuents and the set A of elementary act... |

172 |
M.: Acyclic programs
- Apt, Bezem
- 1991
(Show Context)
Citation Context ... the domain's orphans. Program 0 has many attractive mathematical and computational properties. For instance it is easy to check that, for any database X 2 C 0 , the program R 0 = 0 [X is acyclic [3=-=-=-], i.e. there is a function jj jj from ground atoms of (R 0 ) to natural numbers 4 such that for any atom l occurring in the body of a rule with the head l 0 , jjl 0 jj > jjljj. Acyclic programs not c... |

149 | Ramification and causality - Thielscher - 1997 |

142 | Consistency of clark's completion and existence of stable models
- Fages
- 1994
(Show Context)
Citation Context ...splitting sets. This more powerful version can be used to prove the uniqueness of answer set for locally stratied logic programs [62], existence of answer sets for order-consistent logic programs of [=-=23]-=-, etc. The above results, combined with Proposition 2.2 can be used to establish existence and uniqueness of answer sets of programs with :. Consider for instance program h from the previous section a... |

130 | Planning for temporally extended goals
- Bacchus, Kabanza
- 1996
(Show Context)
Citation Context ...anner. To illustrate the idea let us show how this type of heuristic information can be used in blocks world planning. The rules, R, below express \do not destroy a good tower" heuristic suggeste=-=d in-=- [6]. It ensures that the moves of blocks which satisfy the planner's goal are immediately cut from its search space. h(ok(t); T )s0 T n: h(ok(B 1 ); T )s0 T n; g(on(B 1 ; B 2 )); h(on(B 1 ; B 2 )... |

114 | Encoding planning problems in nonmonotonic logic programs - Dimopoulos, Nebel, et al. - 1997 |

109 |
On stratified autoepistemic theories
- Gelfond
- 1987
(Show Context)
Citation Context ... jjhead(r)jj; 2. For any l 2 neg(r) jjljjsjjhead(r)jj. 14 This is a special case of the notion of stratied general logic program introduced in [2]. The results of that paper together with those from [=-=-=-26] imply that a stratied logic program has exactly one answer set. Forsnite stratied programs this can be easily obtained by induction on the number of levels of with the use of the Splitting Lemma.... |

102 | A Deductive System for Nonmonotonic Reasoning
- Eiter, Leone, et al.
- 1997
(Show Context)
Citation Context ... DA-Prolog. Some of them use the topdown or bottom-up methods of answering queries similar to those in non-disjunctive logic programs [71, 5]. A dierent approach is taken by the dlv reasoning system [=-=17]-=- which takes as an input a program of DA-Prolog with asnite Herbrand Universe and computes the answer sets of this program. The following examples demonstrate the use of disjunction for knowledge repr... |

87 |
Signed data dependencies in logic programs
- Kunen
- 1989
(Show Context)
Citation Context ... 13, 77]. Signed Programs In this section we introduce the notion of signing of a program of A-Prolog. The notion of signing forsnite logic programs without classical negation was introduced by Kunen =-=[3-=-9], who used it as a tool in his proof that, for a certain class of program, two dierent semantics of logic programs coincide. Turner, in [75], extends the denition to the class of logic programs with... |

84 | The expressive powers of logic programming semantics
- Schlipf
- 1995
(Show Context)
Citation Context ...m 5.1 1. The problem of deciding whether a program of FA-Prolog has an answer set is NP-complete [47]. 2. A decision problem P can be solved by a uniform program of FA-Prolog i it is in the class NP [=-=-=-68] 3. A decision problem P can be solved by a uniform program of FDA-Prolog i it is in the complexity class P 2 [11] It is interesting to note that the problem from example 5.2 is P 2 complete [16]... |

84 | Representing actions in logic programs and default theories
- Turner
- 1997
(Show Context)
Citation Context ...s" to this union. The above denition is from [49] and is the product of a long investigation of the nature of causality. (See for instance, [42].) The following theorem (a version of the result f=-=rom [76]-=-) shows the remarkable relationship between causality and beliefs of rational agents as captured by the notion of answer sets of logic programs. First we need some terminology. We start by describing ... |

81 | Efficient top-down computation of queries under the well-founded semantics
- Chen, Swift, et al.
- 1995
(Show Context)
Citation Context ...rty allows the use of SLDNF based methods for answering A-Prolog's queries. Similar observations hold for bottom up methods of computation used in deductive databases. The newer methods (like that of =-=[12]-=-) combine both, bottom-up and top-down, approaches. A more detailed discussion of these matters can be found in [41]. In the last few years we witnessed the coming of age of inference engines aimed at... |

80 | Reasoning agents in dynamic domains - Baral, Gelfond - 1993 |

75 |
Constructible falsity
- Nelson
- 1949
(Show Context)
Citation Context ...logic programs without negation as failure but with :. They demonstrated that in this context logic programs can be viewed as theories of a variant of intuitionistic logic with strong negation due to =-=[55-=-]. For more recent work on this subject see [61]. I believe that both views proved to be fruitful and continue to play an important role in our understanding of A-Prolog. A somewhat dierent view on th... |

74 | Extending the smodels system with cardinality and weight constraints
- Simons
- 2000
(Show Context)
Citation Context ...iled discussion of these matters can be found in [41]. In the last few years we witnessed the coming of age of inference engines aimed at computing answer sets (stable models) of programs of A-Prolog =-=[57, 58, 18-=-]. The algorithms implemented in these engines have much in common with more traditional satisability algorithms. The additional power comes from the use of techniques from deductive databases, good u... |

73 | Disjunctive defaults
- Gelfond, Lifschitz, et al.
- 1991
(Show Context)
Citation Context ... of answer set semantics to represent reasoning by cases and to nicely combine disjunction with defaults. (For comparison of these properties with the use of disjunction in Reiter's default logic see =-=[30]-=-). 20 The next example from [11] demonstrates the expressive power of the language. Example 5.2 Suppose a holding owns some companies producing a set of products. Each product is produced by at most t... |

71 | Default reasoning system deres - Cholewinski, Marek, et al. - 1996 |

70 | An a-prolog decision support system for the space shuttle, 2001. submitted for publication
- Balduccini, Gelfond, et al.
(Show Context)
Citation Context ...one precondition then A is deterministic. A-Prolog's inference engines like Smodels, DLV, and CCALC are suciently powerful to make this method work for comparatively big applications. For instance in =-=[59]-=- the authors used this method for the development of a decision support system to be used by thesight 34 controllers of the space shuttle. One of the system's goals was tosnd the emergency plans for p... |

66 | Developing a declarative rule language for applications in product configuration
- Soininen, Niemelä
- 1998
(Show Context)
Citation Context ...r eciency and power combined with so called answer sets programming paradigm [56], [48] lead to the development of A-Prolog based solutions for various problems in several knowledge intensive domains =-=[70, 59, 22]-=-. This paper is an attempt to introduce the reader to some recent developments in theory and practice of A-Prolog. In section 2 we brie y review the syntax and the semantics of the basic version of A-... |

61 | Declarative problem-solving using the DLV system
- Eiter, Faber, et al.
- 2000
(Show Context)
Citation Context ...iled discussion of these matters can be found in [41]. In the last few years we witnessed the coming of age of inference engines aimed at computing answer sets (stable models) of programs of A-Prolog =-=[57, 58, 18-=-]. The algorithms implemented in these engines have much in common with more traditional satisability algorithms. The additional power comes from the use of techniques from deductive databases, good u... |

57 | L.M.: Reasoning with logic programming
- Alferes, Pereira
(Show Context)
Citation Context |

54 | Action languages, answer sets and planning - Lifschitz - 1999 |

52 |
Representing Actions I: Laws, Observations and Hypothesis
- Baral, Gelfond, et al.
- 1994
(Show Context)
Citation Context ...s of the part of the natural language that are used for describing the behavior of dynamic domains. A theory in an action language normally consists of an action description and a history description =-=[-=-8], [44]. The former contains the knowledge about eects of actions, the latter consists of observations of an agent. Specifying eects of actions An action description language contains propositions wh... |

50 | On the logic of causal explanation
- Lifschitz
- 1997
(Show Context)
Citation Context ...inertia". The application of Cn(Z) adds the \indirect eects" to this union. The above denition is from [49] and is the product of a long investigation of the nature of causality. (See for in=-=stance, [42]-=-.) The following theorem (a version of the result from [76]) shows the remarkable relationship between causality and beliefs of rational agents as captured by the notion of answer sets of logic progra... |

47 | Reasoning with prioritized defaults, in
- Gelfond, Son
- 1998
(Show Context)
Citation Context ...senting defaults in A-Prolog. More detailed discussion of this methodology can be found in [7]. A more general approach which provides means for specifying priorities between defaults can be found in =-=[33-=-], [20]. Since we assume that in databases from C 0 a live person P has a complete record of his/her parents we have that for every person R dierent from the father of P the answer to query father(R; ... |

47 | Relating stable models and ai planning domains - Subrahmanian, Zaniolo - 1995 |

42 | Default logic as a query language
- Cadoli, Eiter, et al.
- 1997
(Show Context)
Citation Context ...esent reasoning by cases and to nicely combine disjunction with defaults. (For comparison of these properties with the use of disjunction in Reiter's default logic see [30]). 20 The next example from =-=[11]-=- demonstrates the expressive power of the language. Example 5.2 Suppose a holding owns some companies producing a set of products. Each product is produced by at most two companies. We will use a rela... |