### Citations

1847 | The stable model semantics for logic programming.
- Gelfond, Lifschitz
- 1988
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Citation Context ...gram Π are defined as the answer sets of the FOL-representation of Π. Proposition 1 from [1] shows that, for normal logic programs, this definition is equivalent to the definition of answer sets from =-=[21]-=-.As shown in [19], the extended notion of SM by a partial list of intensional predicates is not essential in the sense that it can be rewritten so that intensional predicates become exactly those tha... |

1069 |
Negation as failure.
- Clark
- 1978
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Citation Context ...sed on classical logic, one defined by Miller and Shanahan [12], and the other by Mueller [13], which is a simplified version of the former. The fact that circumscription can be reduced to completion =-=[14]-=- under certain syntactic conditions ([15, Proposition 2]) allowed efficient satisfiability solvers (SAT) to be used for event calculus reasoning [16; 13], similar to the idea of SAT-based answer set p... |

965 |
Circumscription—a form of non-monotonic reasoning.
- McCarthy
- 1980
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Citation Context ...(Translation ec2asp). 5 We understand an axiom such as Happens(e, t) as an abbreviation for implication ⊤ → Happens(e, t).1. Simplify all the definitional axioms of the form ∀x(p(x) def ↔ ∃yG(x, y)) =-=(2)-=- except for CC1 − CC4, where y is a list of all free variables in G that are not in x, as ∀xy(G(x, y) → p(x)). 2. For each axiom that contains existential quantifiers, repeat the following until there... |

762 |
A logic-based calculus of events.
- Kowalski, Sergot
- 1986
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Citation Context ...d efficient satisfiability solvers (SAT) to be used for event calculus reasoning [16; 13], similar to the idea of SAT-based answer set programming. Interestingly, early versions of the event calculus =-=[17]-=- were based on logic programs but this was the time before the invention of the stable model semantics, while more extensive later developments of the event calculus were carried out under the classic... |

532 | Applications of Circumscription to Formalizing Common Sense Knowledge” Artificial Intelligence,
- McCarthy
- 1986
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Citation Context ...ive occurrences of ∃yG(x, y) in the axiom, where x is the list of all free variables of ∃yG(x, y), by the formula ¬¬pG(x) where pG is a new predicate constant, and add the axiom ∀xy(G(x, y) → pG(x)). =-=(3)-=- 3. Add choice formulas ∀x(p(x)∨¬p(x)) for all the predicate constants p except for {Initiates, Terminates, Releases, Happens, Ab1, . . . , Abn, p1, p2} where – p1 is a list of all predicate constants... |

137 | Nested expressions in logic programs.
- Lifschitz, Tang, et al.
- 1999
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Citation Context ..., Ab1, . . . , Abn, p1, p2} where – p1 is a list of all predicate constants p considered in Step 1. – p2 is a list of all new predicate constants pG introduced in Step 2. 4. Apply the conversion from =-=[24]-=- that turns programs with nested expressions into disjunctive logic programs. For example, consider DEC5 axiom: ∀ft((HoldsAt(f, t) ∧ ¬ReleasedAt(f, t+1)∧ ¬∃e(Happens(e, t) ∧ Terminates(e, f, t))) → Ho... |

98 |
Commonsense reasoning.
- Mueller
- 2006
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Citation Context ...representation. First, we identify the logical connectives— the comma, the semicolon, and not with their counterparts in classical logic ∧, 3 The last formula is a minor rewriting of the formula from =-=[18]-=- which is Happens(e1, t) ∧ γ → [¬]Happens(e2, t). This rewriting simplifies the later presentation. 4 Due to lack of space, we refer the reader to [18, Chapter 2] for these axioms.∨ and ¬. The FOL-re... |

81 | A circumscriptive calculus of events.
- Shanahan
- 1995
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Citation Context ... formalisms, circumscription and the stable model semanticshave served to provide (different) solutions to the frame problem. A group of action formalisms, such as the classical logic event calculus =-=[7]-=- and temporal action logic [8], take (monotonic) first-order logic as the basis, augmented with circumscription to handle the frame problem. On the other hand, action language A and many of its descen... |

77 | A new perspective on stable models.
- Ferraris, Lee, et al.
- 2007
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Citation Context ...d implementations of the event calculus. We prove the correctness of our translation method and compare our work with the related work by Mueller. 1 Introduction Recently, Ferraris, Lee and Lifschitz =-=[1]-=- presented a generalized definition of a stable model that applies to the syntax of arbitrary first-order sentences. Under this framework, a logic program is viewed as a special class of first-order s... |

71 | Stable models and circumscription.
- Ferraris, Lee, et al.
- 2011
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Citation Context ...the classical logic event calculus can be embedded into logic programs. 3 Review of the New Stable Model Semantics and the New Splitting Theorem Under the new definition of stable models presented in =-=[19]-=- that is applicable to arbitrary first-order sentences, a logic program is identified as a universal formula, called the FOL-representation. First, we identify the logical connectives— the comma, the ... |

57 | The event calculus in classical logicalternative axiomatizations.
- Miller, Shanahan
- 1999
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Citation Context ...models. Note that the event calculus is a family of languages with some variance. Here we consider versions of the event calculus that are based on classical logic, one defined by Miller and Shanahan =-=[12]-=-, and the other by Mueller [13], which is a simplified version of the former. The fact that circumscription can be reduced to completion [14] under certain syntactic conditions ([15, Proposition 2]) a... |

52 | TAL: Temporal action logics language specification and tutorial.
- Doherty, Gustafsson, et al.
- 1998
(Show Context)
Citation Context ...nd the stable model semanticshave served to provide (different) solutions to the frame problem. A group of action formalisms, such as the classical logic event calculus [7] and temporal action logic =-=[8]-=-, take (monotonic) first-order logic as the basis, augmented with circumscription to handle the frame problem. On the other hand, action language A and many of its descendants [9] refer to logic progr... |

36 | Event calculus reasoning through satisfiability.
- Mueller
- 2004
(Show Context)
Citation Context ...culus is a family of languages with some variance. Here we consider versions of the event calculus that are based on classical logic, one defined by Miller and Shanahan [12], and the other by Mueller =-=[13]-=-, which is a simplified version of the former. The fact that circumscription can be reduced to completion [14] under certain syntactic conditions ([15, Proposition 2]) allowed efficient satisfiability... |

28 | A reductive semantics for counting and choice in answer set programming.
- Lee, Lifschitz, et al.
- 2008
(Show Context)
Citation Context ...ed first-order languages (Section 2.4 of [15]). We define RASPL M programs as a special class of sentences under this extension, which are essentially a many-sorted extension of RASPL-1 programs from =-=[23]-=-. We assume that the underlying signature contains an integer sort and contains several built-in symbols, such as integer constants, built-in arithmetic functions +, −, and comparison operators <, ≤, ... |

25 |
A Study of Nonmonotonic Reasoning
- Lin
- 1991
(Show Context)
Citation Context ...ls, not restricted to Herbrand models. The new definition is similar to the definition of circumscription [2; 3], and was even characterized in terms of circumscription [1], extending the work by Lin =-=[4]-=-. The same characterization was also independently given in [5]. The opposite direction, turning (parallel) circumscription into the stable model semantics, was shown in [6], limited to the propositio... |

25 | Loop formulas for circumscription.
- Lee, Lin
- 2006
(Show Context)
Citation Context ... extending the work by Lin [4]. The same characterization was also independently given in [5]. The opposite direction, turning (parallel) circumscription into the stable model semantics, was shown in =-=[6]-=-, limited to the propositional case. In this paper, we start with generalizing this result: turning first-order circumscription into the generalized language of stable models. This leads to the follow... |

20 |
Event calculus planning through satisfiability.
- Shanahan, Witkowski
- 2004
(Show Context)
Citation Context ... that circumscription can be reduced to completion [14] under certain syntactic conditions ([15, Proposition 2]) allowed efficient satisfiability solvers (SAT) to be used for event calculus reasoning =-=[16; 13]-=-, similar to the idea of SAT-based answer set programming. Interestingly, early versions of the event calculus [17] were based on logic programs but this was the time before the invention of the stabl... |

15 |
A first order nonmonotonic extension of constructive logic.
- Pearce, Valverde
- 2005
(Show Context)
Citation Context ...f F . Among those stable models we call the Herbrand models of signature σ, the answer sets of F . The definition of stable models is closely related to the definition of quantified equilibrium model =-=[20; 1]-=-. The answer sets of a logic program Π are defined as the answer sets of the FOL-representation of Π. Proposition 1 from [1] shows that, for normal logic programs, this definition is equivalent to the... |

8 | On the relation between situation calculus and event calculus.
- Belleghem, Denecker, et al.
- 1997
(Show Context)
Citation Context ...nder the stable model semantics (a.k.a. answer set programs) as the underlying formalism. Although there have been some papers that relate classical logic based action formalisms to each other (e.g., =-=[10; 11]-=-), not much work was done in relating them to action languages and to answer set programs. As an initial step, we show how to turn the classical logic event calculus into the general language of stabl... |

8 | A tool for satisfiability-based commonsense reasoning in the event calculus
- Mueller
(Show Context)
Citation Context ...ison with the DEC Reasoner The DEC reasoner 9 is an implementation of the event calculus written by Erik Mueller. The system reduces event calculus reasoning into satisfiability and calls SAT solvers =-=[25]-=-. Since circumscription is not always reducible to completion, some event calculus axioms like effect constraints and disjunctive event axioms 8 Our version of EC/DEC axioms is available at http://rea... |

6 | Event calculus and temporal action logics compared
- Mueller
- 2006
(Show Context)
Citation Context ...nder the stable model semantics (a.k.a. answer set programs) as the underlying formalism. Although there have been some papers that relate classical logic based action formalisms to each other (e.g., =-=[10; 11]-=-), not much work was done in relating them to action languages and to answer set programs. As an initial step, we show how to turn the classical logic event calculus into the general language of stabl... |

1 |
V.: Action languages. 11
- Gelfond, Lifschitz
- 1998
(Show Context)
Citation Context ...emporal action logic [8], take (monotonic) first-order logic as the basis, augmented with circumscription to handle the frame problem. On the other hand, action language A and many of its descendants =-=[9]-=- refer to logic programs under the stable model semantics (a.k.a. answer set programs) as the underlying formalism. Although there have been some papers that relate classical logic based action formal... |

1 |
R.: Two types of splitting in the theory of stable models. Unpublished Draft
- Ferraris, Lee, et al.
- 2008
(Show Context)
Citation Context ...∧ G has a loop l such that – l is contained in p, – l contains an element of h(F ), and – l contains an element of h(G). The following theorem shows how formula SM[F ∧ G; p] can be split : Theorem 1 (=-=[22]-=-) If F and G don’t interact on p, then SM[F ∧ G; p] is equivalent to(a) SM[F ; p \ h(G)] ∧ SM[G; p \ h(F )], and to (b) SM[F ; p \ h(G)] ∧ SM[G; p ∩ h(G)], and to (c) SM[F ; p ∩ h(F )] ∧ SM[G; p ∩ h(... |