## An Overview of Temporal and Modal Logic Programming (1994)

Venue: | Proc. First Int. Conf. on Temporal Logic - LNAI 827 |

Citations: | 60 - 6 self |

### BibTeX

@INPROCEEDINGS{Orgun94anoverview,

author = {Mehmet A. Orgun and Wanli Ma},

title = {An Overview of Temporal and Modal Logic Programming},

booktitle = {Proc. First Int. Conf. on Temporal Logic - LNAI 827},

year = {1994},

pages = {445--479},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion. Categories: Temporal and Modal Logic Programming. 1 Introduction In logic programming, a program is a set of Horn clauses representing our knowledge and assumptions about some problem. The semantics of logic programs as developed by van Emden and Kowalski [96] is based on the notion of the least (minimum) Herbrand model and its fixed-point characterization. As logic programming has been applied to a growing number of problem domai...

### Citations

2293 | Maintaining Knowledge about Temporal Intervals - Allen - 1983 |

1856 |
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Citation Context ...ng with infinite terms does not have a minimum model semantics and therefore the intended meaning of an infinitary logic program is not characterized by the set of logical consequences of the program =-=[97, 64]-=-. And this is a major problem: what an infinitary program does is not what it says declaratively. But then how can we attack problems from different domains and still keep the declarative features of ... |

1213 |
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Citation Context ...rms of intensional logic. There are a number of modal and temporal logic programming languages: Tempura [70, 52] and Tokio [9] are based on interval logic; THLP [99, 100], Chronolog [83, 74], Templog =-=[3, 4]-=- and Temporal Prolog [44] are based on temporal logic; there is also another Temporal Prolog [54] based on reified temporal logic; Brzoska [26] proposed temporal logic programming based on metric temp... |

786 | Constraint logic programming
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Citation Context ... called TL1, in which the only temporal operator is the next-time operator fl [18, section 5]. Brzoska [25] showed that Templog can be considered as an instance of the CLP scheme of Jaffar and Lassez =-=[58]-=- over a suitable algebra A. Templog programs are translated into classical logic programs and Templog goals into classical goals through a meaning preserving transformation, \Pi. Translated programs c... |

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Citation Context ...)modal logics. This classification is naturally provided by the logics these languages are based upon. The paper concludes with a brief summary and discussion. 2 Temporal and Modal Logics Modal logic =-=[56, 29]-=- is the study of context-dependent properties such as necessity and possibility. In modal logic, the meaning of expressions depends on an implicit context, abstracted away from the object language. Te... |

710 | The semantics of predicate logic as a programming language
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Citation Context ...ral reasoning, deductive databases, knowledge representation, and dataflow computation. On the other hand, we would like to remain true to the original goals of logic programming outlined by Kowalski =-=[61]-=-: Logic programs should specify only what is to be computed; not how it is to be computed. In order to overcome some of the limitations of logic programming, many non-logical constructs in the form of... |

634 |
Modal Logic: An Introduction
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Citation Context ...)modal logics. This classification is naturally provided by the logics these languages are based upon. The paper concludes with a brief summary and discussion. 2 Temporal and Modal Logics Modal logic =-=[56, 29]-=- is the study of context-dependent properties such as necessity and possibility. In modal logic, the meaning of expressions depends on an implicit context, abstracted away from the object language. Te... |

488 |
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Citation Context ... head of a clause. In [14, 15], it is reported that a prototype implementation of TIM was written in LISP, and a compiled version in C, following the same principles as WAM (Warren's Abstract Machine =-=[102, 5]-=-). The underlying abstract machine of TIM implementations is called TARSKI (Toulouse Abstract Reasoning System for Knowledge Inference). These implementations of TIM led to a distributed implementatio... |

269 |
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Citation Context ... overcome some of the limitations of logic programming, many non-logical constructs in the form of annotations, extra system predicates, and infinitary objects have been introduced; for instance, see =-=[91]-=- for a comprehensive survey on concurrent logic languages. These languages are an important contribution to the field of programming languages and their implementations, but the problem with them is t... |

231 |
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Citation Context ... of context-dependent properties such as necessity and possibility. In modal logic, the meaning of expressions depends on an implicit context, abstracted away from the object language. Temporal logic =-=[82, 28]-=- can be regarded as an instance of modal logic where the collection of contexts models a collection of moments in time. Therefore the following discussion on modal logic also applies to temporal logic... |

177 |
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Citation Context ...e modal and/or epistemic logics? These logics have been extensively studied in philosophy and mathematics and applied in many problem domains (including those in artificial intelligence) with success =-=[8, 57, 92, 93]-=-. Therefore we advocate extending logic programming with temporal and modal logics (or with other non-classical logics) whenever appropriate. Recently, several researchers have proposed extending logi... |

154 | Executing temporal logic programs
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Citation Context ...earchers have proposed extending logic programming with temporal logic, modal logic and other forms of intensional logic. There are a number of modal and temporal logic programming languages: Tempura =-=[70, 52]-=- and Tokio [9] are based on interval logic; THLP [99, 100], Chronolog [83, 74], Templog [3, 4] and Temporal Prolog [44] are based on temporal logic; there is also another Temporal Prolog [54] based on... |

135 |
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Citation Context ... terms of an accessibility relation alone. There are more general approaches to the semantics of modal logic, including "neighborhood" semantics which is usually attributed to Scott [90] and=-= Montague [69]-=-. For a detailed exposition of more general approaches and their relative strengths, we refer the reader to the literature, for example, see [27] and [103]. Neighborhood semantics is used in [77] to p... |

123 | Two-Dimensional Modal Logic - Segerberg - 1973 |

85 | A resolution calculus for modal logics
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Citation Context ...in modal logic programs, rather it directly encodes the accessibility relations into the unification algorithm. This encoding technique is borrowed from Ohlbach's resolution calculus for modal logics =-=[71]-=-. It is claimed that the encoding technique improves the efficiency of the implementations (meta-interpreters) of modal logic programming, but it requires special unification algorithms for different ... |

81 |
A Temporal Fixpoint Calculus
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Citation Context ...d on temporal Herbrand models, and its fixed-point characterization. It is also shown that the expressiveness of Templog queries, in the propositional case, corresponds to a fragment of ��TL of Va=-=rdi [98]-=- allowing only least fixed-points to be applied to positive formulas. Note that Templog is in fact equivalent in expressive power to a fragment of itself, called TL1, in which the only temporal operat... |

80 |
Basic tense logic
- Burgess
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(Show Context)
Citation Context ... of context-dependent properties such as necessity and possibility. In modal logic, the meaning of expressions depends on an implicit context, abstracted away from the object language. Temporal logic =-=[82, 28]-=- can be regarded as an instance of modal logic where the collection of contexts models a collection of moments in time. Therefore the following discussion on modal logic also applies to temporal logic... |

77 |
A.: “Verification of concurrent programs: The temporal framework”; in The correctness problem in computer science
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(Show Context)
Citation Context ...ing) and the dynamic properties of certain problems such as simulation, why not use temporal logic in the first place? Temporal logics have already been used in program specification and verification =-=[65, 63]-=-, temporal reasoning [86, 32], and temporal databases [34, 95, 47]. Or if we want to model knowledge and belief, why not use modal and/or epistemic logics? These logics have been extensively studied i... |

74 |
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- Scott
- 1970
(Show Context)
Citation Context ...We could extend it with extra modalities in the obvious way, by allowing a family of dual pairs, each with its own accessibility relation. This is better but still not truly general because, as Scott =-=[90]-=- and others have pointed out, there are many natural modal operators that cannot be defined in terms of an accessibility relation alone. There are more general approaches to the semantics of modal log... |

74 |
the dataflow programming language
- LUCID
- 1985
(Show Context)
Citation Context ... 100] proposed a tensed extension of Horn logic programming (called THLP), which was later developed into Chronolog [74, 76, 83]. The design of Chronolog was influenced by the dataflow language Lucid =-=[101]-=-. Hence its original target application was modelling non-terminating dataflow computations. Chronolog has two temporal operators (borrowed from Lucid): first refers to the initial moment in time, and... |

69 |
Temporal Logics of Programs
- Kröger
- 1985
(Show Context)
Citation Context ...ing) and the dynamic properties of certain problems such as simulation, why not use temporal logic in the first place? Temporal logics have already been used in program specification and verification =-=[65, 63]-=-, temporal reasoning [86, 32], and temporal databases [34, 95, 47]. Or if we want to model knowledge and belief, why not use modal and/or epistemic logics? These logics have been extensively studied i... |

66 |
Paraconsistent logic programming
- Blair, Subrahmanian
- 1989
(Show Context)
Citation Context ...l logic programming based on Kripke-style semantics for modal logic, and investigated the connections between logic programming and dynamic logic. Another general framework is provided by Blair et al =-=[24, 22]-=- for non-classical extensions of logic programming. We believe that the utility of temporal and modal logic programming has been demonstrated in the works reviewed in this paper; we are, however, yet ... |

64 |
The WAM: A (real) tutorial
- Aït-Kaci
- 1990
(Show Context)
Citation Context ... head of a clause. In [14, 15], it is reported that a prototype implementation of TIM was written in LISP, and a compiled version in C, following the same principles as WAM (Warren's Abstract Machine =-=[102, 5]-=-). The underlying abstract machine of TIM implementations is called TARSKI (Toulouse Abstract Reasoning System for Knowledge Inference). These implementations of TIM led to a distributed implementatio... |

62 | Temporal deductive databases
- Baudinet, Chomicki, et al.
- 1993
(Show Context)
Citation Context ...function, and can be viewed as interpreted over the natural numbers. The effects of temporal operators of TL1 are simulated by manipulating the extra time parameters in predicates. It is mentioned in =-=[19]-=- that Datalog 1S can be considered as a syntactical variant of (function-free) Templog, because Templog programs can be translated into TL1 programs. It is also mentioned in [19] that there is a trans... |

56 |
Formal semantics for time in databases
- Clifford, Warren
- 1983
(Show Context)
Citation Context ...mulation, why not use temporal logic in the first place? Temporal logics have already been used in program specification and verification [65, 63], temporal reasoning [86, 32], and temporal databases =-=[34, 95, 47]-=-. Or if we want to model knowledge and belief, why not use modal and/or epistemic logics? These logics have been extensively studied in philosophy and mathematics and applied in many problem domains (... |

48 |
The power of temporal proofs
- Abadi
(Show Context)
Citation Context ... modal logic programming languages Results on the completeness of temporal and modal logic programming are very encouraging, given that first-order temporal and modal logics are inherently incomplete =-=[1, 94]-=-. We now know that there are complete subsets of temporal and modal logics which can be used as the basis of logic programming. In standard logic programming, the declarative and operational semantics... |

47 |
Modal theorem proving: An equational viewpoint
- Auffray, Enjalbert
- 1992
(Show Context)
Citation Context ... of negation in the heads of program clauses. Multimodal Logic Programming (Debart et al, 1992): Debart et al [36] extended the automated theorem proving method in modal logic of Aufray and Enjalbert =-=[12]-=- to multimodal logic. The resulting method is called \Sigma -E-resolution. Then a restricted version of \Sigma -E-resolution is applied to modal logic programming. Modal logics considered are KD, KT, ... |

39 |
Temporal Logic & Historical Databases
- Gabbay, McBrien
- 1991
(Show Context)
Citation Context ...mulation, why not use temporal logic in the first place? Temporal logics have already been used in program specification and verification [65, 63], temporal reasoning [86, 32], and temporal databases =-=[34, 95, 47]-=-. Or if we want to model knowledge and belief, why not use modal and/or epistemic logics? These logics have been extensively studied in philosophy and mathematics and applied in many problem domains (... |

38 |
Temporal relational algebra as a basis for temporal relational completeness
- Tuzhilin, Clifford
- 1990
(Show Context)
Citation Context ...mulation, why not use temporal logic in the first place? Temporal logics have already been used in program specification and verification [65, 63], temporal reasoning [86, 32], and temporal databases =-=[34, 95, 47]-=-. Or if we want to model knowledge and belief, why not use modal and/or epistemic logics? These logics have been extensively studied in philosophy and mathematics and applied in many problem domains (... |

35 |
Theory of Logical Calculi
- Wójcicki
- 1988
(Show Context)
Citation Context ...usually attributed to Scott [90] and Montague [69]. For a detailed exposition of more general approaches and their relative strengths, we refer the reader to the literature, for example, see [27] and =-=[103]-=-. Neighborhood semantics is used in [77] to provide a unifying theoretical framework for intensional (temporal and modal) logic programming languages. In most of the other reported works, the standard... |

34 |
Modal and temporal logic programming
- Gabbay
- 1987
(Show Context)
Citation Context ...here are a number of modal and temporal logic programming languages: Tempura [70, 52] and Tokio [9] are based on interval logic; THLP [99, 100], Chronolog [83, 74], Templog [3, 4] and Temporal Prolog =-=[44]-=- are based on temporal logic; there is also another Temporal Prolog [54] based on reified temporal logic; Brzoska [26] proposed temporal logic programming based on metric temporal logic; Molog [39] is... |

32 |
Temporal logic programming is complete and expressive
- Baudinet
- 1989
(Show Context)
Citation Context ...tics for logic programming. The declarative and operational semantics of some of these languages have already been worked out, and some languages have already been implemented. For instance, Baudinet =-=[16, 17, 18]-=- shows the completeness of the proof procedure of Templog and provides the declarative semantics of Templog programs. Orgun and Wadge [74, 75, 76] develop the model-theoretic semantics of Chronolog an... |

32 |
Multimodal logic programming using equational and order-sorted logic. Theoretical Computer Science
- Debart, Enjalbert, et al.
- 1992
(Show Context)
Citation Context ...log [87] is based on modal logic; InTense [68] is a multi-dimensional language with temporal and spatial dimensions. There are also some multi-modal approaches to temporal and modal logic programming =-=[7, 36]-=-. Some other non-classical extensions of logic programming include multiple-valued logic programming schemes of Blair et al [24] and of Fitting [43]. However, these two approaches deal with non-classi... |

28 |
Proving Termination Properties of Prolog Programs: A Semantic Approach
- Baudinet
- 1992
(Show Context)
Citation Context ...ams. In order to give a formal semantics to Tokio, one would need to combine the semantics of ITL with a semantics of Prolog that explicitly represents the execution mechanism (e.g., that of Baudinet =-=[20]-=-). Below are some examples of Tokio sentences and the results of their execution: 1. length(2), @write(0) && length(2), #write(1). Time 0 1 2 3 4 Result -- 0 1 1 1 2. length(5), !?write(1). Time 0 1 2... |

27 |
Logic Programming on a Topological Bilattice
- Fitting
- 1988
(Show Context)
Citation Context ...proaches to temporal and modal logic programming [7, 36]. Some other non-classical extensions of logic programming include multiple-valued logic programming schemes of Blair et al [24] and of Fitting =-=[43]-=-. However, these two approaches deal with non-classical semantics for logic programming. The declarative and operational semantics of some of these languages have already been worked out, and some lan... |

24 |
Temporal logic programming and its relation to constraint logic programming
- Brzoska
- 1991
(Show Context)
Citation Context ...ve formulas. Note that Templog is in fact equivalent in expressive power to a fragment of itself, called TL1, in which the only temporal operator is the next-time operator fl [18, section 5]. Brzoska =-=[25]-=- showed that Templog can be considered as an instance of the CLP scheme of Jaffar and Lassez [58] over a suitable algebra A. Templog programs are translated into classical logic programs and Templog g... |

24 |
Temporal logic programming with metric and past operators
- Brzoska
(Show Context)
Citation Context ...val logic; THLP [99, 100], Chronolog [83, 74], Templog [3, 4] and Temporal Prolog [44] are based on temporal logic; there is also another Temporal Prolog [54] based on reified temporal logic; Brzoska =-=[26]-=- proposed temporal logic programming based on metric temporal logic; Molog [39] is based on user-elected modal logics; Modal Prolog [87] is based on modal logic; InTense [68] is a multi-dimensional la... |

24 |
del Cerro. MOLOG: A system that extends PROLOG with modal logic
- Fariñas
- 1986
(Show Context)
Citation Context ...og [44] are based on temporal logic; there is also another Temporal Prolog [54] based on reified temporal logic; Brzoska [26] proposed temporal logic programming based on metric temporal logic; Molog =-=[39]-=- is based on user-elected modal logics; Modal Prolog [87] is based on modal logic; InTense [68] is a multi-dimensional language with temporal and spatial dimensions. There are also some multi-modal ap... |

23 |
Temporal logic programming language Tokio
- Aoyagi, Fujita, et al.
- 1986
(Show Context)
Citation Context ...sed extending logic programming with temporal logic, modal logic and other forms of intensional logic. There are a number of modal and temporal logic programming languages: Tempura [70, 52] and Tokio =-=[9]-=- are based on interval logic; THLP [99, 100], Chronolog [83, 74], Templog [3, 4] and Temporal Prolog [44] are based on temporal logic; there is also another Temporal Prolog [54] based on reified tempo... |

21 |
Towards a Unified Theory of Intensional Logic Programming
- Orgun, Wadge
- 1992
(Show Context)
Citation Context ...we can replace y by a using the first clause. Temporal Prolog does not enjoy a minimum model semantics because of the use of operators such as F and P in the head of a program clause. Orgun and Wadge =-=[77]-=- showed that F and P are not conjunctive, and that the model intersection property does not hold for (intensional) logic programs when an operator which is not conjunctive is allowed to appear in the ... |

20 |
Lucid - A Formal System for Writing and Proving Programs
- Ashcroft, Wadge
- 1976
(Show Context)
Citation Context ...guage InTense was invented by Mitchell and Faustini [68, 67]. It was inspired by both Chronolog and Lucid [101]. Lucid is a functional programming language, in fact, an intensional extension of ISWIM =-=[11, 101]-=-. In Lucid, as in Tempura, variables represent a sequence of values over the time dimension. InTense has a large repertoire of Lucid-like intensional operators such as asa (as soon as), wvr (whenever)... |

20 |
Tense logic programming: a respectable alternative
- Wadge
(Show Context)
Citation Context ...emporal logic, modal logic and other forms of intensional logic. There are a number of modal and temporal logic programming languages: Tempura [70, 52] and Tokio [9] are based on interval logic; THLP =-=[99, 100]-=-, Chronolog [83, 74], Templog [3, 4] and Temporal Prolog [44] are based on temporal logic; there is also another Temporal Prolog [54] based on reified temporal logic; Brzoska [26] proposed temporal lo... |

18 |
Declarative semantics for modal logic programs
- Balbiani, Herzig
- 1988
(Show Context)
Citation Context ...og and describe a general framework to deal with several intensional programming systems. It is shown in [78] that Chronolog admits a sound and complete resolutiontype proof procedure. Balbiani et al =-=[13]-=- provide a declarative and operational semantics for a class of Molog programs. Gabbay [44] showed the soundness of a computation procedure for Temporal Prolog, based on branching time. Fitting [43] e... |

18 |
A Simple Proof of the Completeness of Temporal Logic Programming
- Baudinet
- 1992
(Show Context)
Citation Context ...tics for logic programming. The declarative and operational semantics of some of these languages have already been worked out, and some languages have already been implemented. For instance, Baudinet =-=[16, 17, 18]-=- shows the completeness of the proof procedure of Templog and provides the declarative semantics of Templog programs. Orgun and Wadge [74, 75, 76] develop the model-theoretic semantics of Chronolog an... |

18 |
Theory and practice of temporal logic programming
- Orgun, Wadge
- 1992
(Show Context)
Citation Context ...have already been implemented. For instance, Baudinet [16, 17, 18] shows the completeness of the proof procedure of Templog and provides the declarative semantics of Templog programs. Orgun and Wadge =-=[74, 75, 76]-=- develop the model-theoretic semantics of Chronolog and describe a general framework to deal with several intensional programming systems. It is shown in [78] that Chronolog admits a sound and complet... |

17 |
Temporal logic programming
- Hale
- 1987
(Show Context)
Citation Context ...earchers have proposed extending logic programming with temporal logic, modal logic and other forms of intensional logic. There are a number of modal and temporal logic programming languages: Tempura =-=[70, 52]-=- and Tokio [9] are based on interval logic; THLP [99, 100], Chronolog [83, 74], Templog [3, 4] and Temporal Prolog [44] are based on temporal logic; there is also another Temporal Prolog [54] based on... |

16 | A Temporal Extension of Prolog, The - Hrycej - 1993 |

16 | Chronolog admits a complete proof procedure
- Orgun, Wadge
- 1993
(Show Context)
Citation Context ...c programming. In standard logic programming, the declarative and operational semantics of logic programs coincide [96, 64]. The completeness results (such as those of Templog [16, 17, 18], Chronolog =-=[74, 78]-=-, Molog [13], MTL [26]) guarantee that the declarative and operational semantics of temporal and modal logic programs of those languages also coincide. As a consequence, we can use the tools and techn... |

15 |
Non-Standard Logics for Automated Reasoning
- Smets, Mamdani, et al.
- 1988
(Show Context)
Citation Context ...e modal and/or epistemic logics? These logics have been extensively studied in philosophy and mathematics and applied in many problem domains (including those in artificial intelligence) with success =-=[8, 57, 92, 93]-=-. Therefore we advocate extending logic programming with temporal and modal logics (or with other non-classical logics) whenever appropriate. Recently, several researchers have proposed extending logi... |

14 |
On the expressiveness of temporal logic programming
- Baudinet
- 1995
(Show Context)
Citation Context ...tics for logic programming. The declarative and operational semantics of some of these languages have already been worked out, and some languages have already been implemented. For instance, Baudinet =-=[16, 17, 18]-=- shows the completeness of the proof procedure of Templog and provides the declarative semantics of Templog programs. Orgun and Wadge [74, 75, 76] develop the model-theoretic semantics of Chronolog an... |