## A Framework for Modal Logic Programming (1996)

Venue: | In Joint International Conference and Symposium on Logic Programming |

Citations: | 18 - 3 self |

### BibTeX

@INPROCEEDINGS{Baldoni96aframework,

author = {Matteo Baldoni and Laura Giordano and Alberto Martelli},

title = {A Framework for Modal Logic Programming},

booktitle = {In Joint International Conference and Symposium on Logic Programming},

year = {1996},

pages = {52--66},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we present a framework for developing modal extensions of logic programming, which are parametric with respect to the properties chosen for the modalities and which allow sequences of modalities of the form [t], where t is a term of the language, to occur in front of clauses, goals and clause heads. The properties of modalities are specified by a set A of inclusion axioms of the form [t 1 ] : : : [t n ]ff oe [s 1 ] : : : [s m ]ff. The language can deal with many of the wellknown modal systems and several examples are provided. Due to its features, it is particularly suitable for performing epistemic reasoning, defining parametric and nested modules, describing inheritance in a hierarchy of classes and reasoning about actions. A goal directed proof procedure of the language is presented, which is modular with respect to the properties of modalities. Moreover, we define a fixpoint semantics, by generalizing the standard construction for Horn clauses, which is used to prov...

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Citation Context ... under certain restriction on such systems it is decidable. For example when the system is complete, i.e., it is noetherian and confluent [6], or when [\Gamma 1 ] RA is a context sensitive language 6 =-=[16]-=-. These remarks are quite relevant when we have to deal with the implementation of the matching relation in the case when only ground terms may occur within modalities in the program, in the goal and ... |

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Citation Context ...c semantics, and it works for the whole class of logics identified by the inclusion axioms. 1 Introduction Modal and temporal extensions of logic programming have recently received a lot of attention =-=[20, 9, 1, 8, 15, 18]-=-, since they provide tools for formalizing temporal and epistemic knowledge and reasoning, while retaining the characterizing properties of logic programming languages, as, for instance, goal directed... |

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Citation Context ...change from a world to another, there is the problem of defining the satisfiability at a world w of a formula ff(t) containing a term t whose interpretation is not in D(w). With this regard we follow =-=[11]-=-, and we do not make any special restriction, like imposing ff(t) to be false in w, or to be undefined. However, when we define satisfiability and validity of a formula we look at the truth value of t... |

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Citation Context ...respect to the axioms A of the logic: the differences among the logics are factored out in the adopted matching relationsA . The proof procedure we define is an abstract one. In particular, we follow =-=[17]-=-, in order to avoid problems with variable renaming and substitutions, we denote by [P ] the set of all ground instances of a given set of clauses in P . Definition 4.1 Let be \Theta a set of clauses ... |

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Citation Context ...ossible worlds (rigid designators). On the contrary, predicate symbols may have a different interpretation at each possible world. For a survey of the different systems for quantified modal logic see =-=[13]-=-. 4 Operational semantics Now that we have defined the class of modal logics underlying the programming languages MA 's, we are ready to introduce a goal directed proof procedure for them. The proof p... |

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Citation Context ...c semantics, and it works for the whole class of logics identified by the inclusion axioms. 1 Introduction Modal and temporal extensions of logic programming have recently received a lot of attention =-=[20, 9, 1, 8, 15, 18]-=-, since they provide tools for formalizing temporal and epistemic knowledge and reasoning, while retaining the characterizing properties of logic programming languages, as, for instance, goal directed... |

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Citation Context ...ending and descending, which contain two different definition of the predicate ordered. Now, we can specify a particular order through the variable Order. Thus, the goal G 1 = [sort(ascending)]busort(=-=[2; 3; 1]-=-; S) succeeds with answer S = [1; 2; 3], while the goal G 2 = [sort(descending)]busort([2; 3; 1]; S) succeeds with answer S = [3; 2; 1]. Example 2.4 (Inheritance and hierarchy) The following example i... |

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Citation Context ...d by axioms of the form [t 1 ] : : : [t n ]ff oe [s 1 ] : : : [s m ]ff: (1) The logics in this class have been called inclusion logics in [14], where a refinement of the functional translation method =-=[19]-=- has been proposed for them. Given a set of inclusion axioms A of the form (1), we define a modal logic programming language, called MA , whose underlying modal logic is the one characterized by those... |

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Citation Context ...ause heads and clause bodies (or goals), existential modal operators are not allowed. In particular, as a difference with other languages proposed in the literature, like TEMPLOG [1], Temporal Prolog =-=[12]-=- and the language in [3], existential modalities are not allowed to occur in front of goals. In spite of this limitation, the features of parametric modalities and the possibility of introducing inclu... |

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Citation Context ...c semantics, and it works for the whole class of logics identified by the inclusion axioms. 1 Introduction Modal and temporal extensions of logic programming have recently received a lot of attention =-=[20, 9, 1, 8, 15, 18]-=-, since they provide tools for formalizing temporal and epistemic knowledge and reasoning, while retaining the characterizing properties of logic programming languages, as, for instance, goal directed... |

24 |
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Citation Context ...ct to the set of chosen axioms A, they work for the whole class of modal languages identified by the inclusion axioms. This framework allows to define modal languages which extend the one proposed in =-=[4]-=- for representing module constructs. In particular, we show an example of how to deal with nested and parametric modules. Moreover, the framework allows to define languages suitable for performing epi... |

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Citation Context ...ending and descending, which contain two different definition of the predicate ordered. Now, we can specify a particular order through the variable Order. Thus, the goal G 1 = [sort(ascending)]busort(=-=[2; 3; 1]-=-; S) succeeds with answer S = [1; 2; 3], while the goal G 2 = [sort(descending)]busort([2; 3; 1]; S) succeeds with answer S = [3; 2; 1]. Example 2.4 (Inheritance and hierarchy) The following example i... |

17 |
Thue systems as rewriting systems
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Citation Context ...em. In general the word problem is undecidable 5 , neverthless under certain restriction on such systems it is decidable. For example when the system is complete, i.e., it is noetherian and confluent =-=[6]-=-, or when [\Gamma 1 ] RA is a context sensitive language 6 [16]. These remarks are quite relevant when we have to deal with the implementation of the matching relation in the case when only ground ter... |

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14 |
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Citation Context ... provided. Instead of developing specific theorem proving techniques for modal logics, many authors have proposed the alternative approach of translating modal logics into classical first order logic =-=[10]-=-, so that standard theorem provers can be used. The translation methods are based on the idea of making explicit reference to the worlds, by adding to all predicates and functions as argument represen... |

9 |
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Citation Context ...context in the operational semantics during a computation. Completeness with respect to the model theory is proved by a Henkin-style canonical model construction, which is similar to the one given in =-=[5]-=-. We also show that there is no loss of generality in restricting Kripke A-interpretations to those in which the domain at each world is the Herbrand universe. It is worth noting that the TA;P operato... |

8 |
Inheritance and Hypothetical Reasoning in Logic Programming
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(Show Context)
Citation Context ... with answer S = [1; 2; 3], while the goal G 2 = [sort(descending)]busort([2; 3; 1]; S) succeeds with answer S = [3; 2; 1]. Example 2.4 (Inheritance and hierarchy) The following example is taken from =-=[7]-=- and describes inheritance in a hierarchy of classes. Let us consider four classes, named, respectively, animal, horse, bird and tweety. Since what is true for animals is also true for birds and horse... |

7 |
Deduction for multimodal logics
- Gasquet
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(Show Context)
Citation Context ...r we will focus on a class of normal modal logics characterized by axioms of the form [t 1 ] : : : [t n ]ff oe [s 1 ] : : : [s m ]ff: (1) The logics in this class have been called inclusion logics in =-=[14]-=-, where a refinement of the functional translation method [19] has been proposed for them. Given a set of inclusion axioms A of the form (1), we define a modal logic programming language, called MA , ... |