The development of languages allowing a proper handling of time is important in many areas of computer science because the capability to deal with the notions of change and time are essential to solve their problems.
In the development of EMTPL [CA99a] we focused the research work in making the languages useful in the area of databases, where some problems demand the possibility to represent and use temporal information. We achieve that goal, although we managed the negation in a way that causes the lost of some properties of the underlying logic. This logic was deeply studied and it is one of the most famous metric temporal logics [Pri67a]. The main idea of this work is to extend EMTPL by the addition of a new operator, and also grant the negation with its logic meaning.Eje: Ingeniería de Software y Base de DatosRed de Universidades con Carreras en Informática (RedUNCI

Cobo, María Laura

Falappa, Marcelo Alejandro

Servicio de Difusión de la Creación Intelectual

An extension to EMTPLMar´ıa Laura Cobo Marcelo Alejandro FalappaDepartment of Computer Science and Engineering ∗Universidad Nacional del SurBah´ıa Blanca - Argentinafax: +54 291 4595136[mlcobo, mfalappa] @cs.uns.edu.arAbstractThe development of languages allowing a proper handling of time is important in manyareas of computer science because the capability to deal with the notions of change and timeare essential to solve their problems.In the development of EMTPL [CA99a] we focused the research work in making thelanguages useful in the area of databases, where some problems demand the possibility torepresent and use temporal information. We achieve that goal, although we managed thenegation in a way that causes the lost of some properties of the underlying logic. This logicwas deeply studied and it is one of the most famous metric temporal logics [Pri67a]. Themain idea of this work is to extend EMTPL by the addition of a new operator, and alsogrant the negation with its logic meaning.Key words: Programming Languages, Metric Temporal Logic, Deductive Databases, Negation.1 IntroductionThe database research field provides solutions for the problem of storing and retrieving infor-mation. One of the possible ways to achieve this goal is by using deductive databases. Theyuse logic as a mean to represent information in a declarative way and an inference procedure toanswer queries. Some problems are involved with the notions of change and time. For examplewe could be interested on keeping record of the different positions of the employees in somefactory, evolution of patients in a hospital, transactions in a business or events in an industryenvironment.Some implementations are available for languages with capability to handle temporal con-cepts, for example, Temporal Prolog in [CA99b] based on the proposal of [Gab87]. The TemporalProlog’s proposal was improved in [CA99a] where we had presented a programming language,Metric Temporal Programming Language (MTPL), with the capability of dealing with more pre-cise temporal information; this language is based on a deeply studied logic proposed by Prior([Pri67a] and [Pri67b]) and follows one of the most known ways of seeing time, through A-series(past, present and future). There are other logics, and some of them formalize the other view oftime, as B-series (before, after), where we use explicit references of time. An example of logic ofthis later type has been presented by Rescher [RU71]. However, there are many circumstanceswhen it is very useful if not mandatory to have both ways to use and refer time.To preserve all the properties and benefits of the underlying logic is important to associatethe logic meaning to the negation operator. In the first version of EMTPL, we use negation as∗Partially supported by the Secretary of Science and Technology (Universidad Nacional del Sur).1Workshop de Investigadores en Ciencias de la Computación WICC 2002Página 2667failure instead of classical negation. Because of this the manipulation of negative informationis not always appropriate, we could think about the need of counting with an operator thatoffers to the language some kind of temporal negation. This new operator could be interesting,because we will count with an operator that provides a way to manage that negative informationthat is vital in some contexts or problems.EMTPL [CA99a] was designed to manipulate temporal references of both kinds, makingthe language appropriate for Databases. In section 2 we present a brief presentation of theprogramming language EMTPL. In section 3 we mention the principal aspects of the extensionwe have in mind. Conclusions and future work suggestions will be presented in section 4.2 Brief revision to EMTPL2.1 Syntax and semanticsThe syntax of the EMTPL’s operators as follows:φ = p|¬φ|φ1 ∧ φ2|ATnφ|3+n φ|∃n 3+n φ|∀n 3+n φ|3−n φ|∃n 3−n φ|∀n 3−n φDisjunction and implication could be defined as usual. More temporal operators are definableas specified below.The intuitive meaning of the temporal operators 3+ and 3− is as follows:3+ φ sometime in the future φ or φ will be true in some moment of the future.3− φ sometime in the past φ or φ was true in some moment of the past.With this intuitive idea we can now give the formal semantic the operators. We assume,then, a set of instants . . . , in, in+1, in+2, . . . that represents an unbounded and linear temporalstructure. The information in the system could be seen as a list of sets, σ, that contains allthe truths we have in our theory. Each member of the list is a set denoted by σ(j). Thenσ(j) represents the set of truths at an instant j. We follow with an inductive definition for “atemporal proposition true at an instant j”. We start specifying that p ∈ σ(j) means “p is trueat instant j”.It is important to point out that the quantification is applied only over the members of thetemporal structure, i.e., the set of numbers we choose to represent time. We claim this set ofnumbers to be a metric space.(σ, j) |= p iff p ∈ σ(j)(σ, j) |= ¬p iff (σ, j) 6|= p(σ, j) |= p∧ q iff (σ, j) |= p and (σ, j) |= q(σ, j) |= 3+c p iff (σ, j + c) |= p(σ, j) |= 3−c p iff (σ, j − c) |= p(σ, j) |= ∃n 3+n p iff exists an instant n, n > 0 such that (σ, j + n) |= p(σ, j) |= ∃n 3−n p iff exists an instant n, n > 0 such that (σ, j − n) |= p(σ, j) |= ∀n 2+n p iff for all instant n, n > 0 we have (σ, j + n) |= p(σ, j) |= ∀n 2−n p iff for all instant n, n > 0 we have (σ, j − n) |= p(σ, j) |= ATc p iff (σ, c) |= pWe can define some other nice operators from this ones [CA00, CA99a]2Workshop de Investigadores en Ciencias de la Computación WICC 2002Página 26782.2 Definition of the languageThe language is based on Prior’s logic [Pri67a, Pri67b] plus an extension to that logic buy theintroduction of the AT . This extension consists mainly, on introducing the AT operator inPrior’s axiomatization [CA99a].In what respects to the language based on this extended logic, Extended Metric TemporalProgramming Language (EMTPL), we define it in this way:Definition 1 (EMTPL)Let us consider a language with propositional atoms, the logic connectives: ∧,∨ →, ¬ and thetemporal operators: 3+n, 3−n, 3+1, 3−, 2+2, 2−. We define the notion of EMTP’s program, clause,always clause, ordinary clause, head, body and goal as follows:• A program is a set of “clauses”.• A clause is ATiC or C where C is an “ordinary clause”.• An ordinary clause is a “head” or a B → H , where B is a “body” and H is a “head”.• A head is an atomic formula, 3+n A or 3−n A or 2+A or 2−A where A is a conjunction of“ordinary clauses”.• A body is an atomic formula, a conjunction of bodies, 3+n B or 3−n B or 2+A or 2−A or ¬Bwhere B is a body.• A goal is ATnB or B where B is any body or a disjunction of bodies.It is important to point out that the facts or rules (Prop) that are not affected with an ATnoperator are interpreted as facts or rules that happen in the present moment, i.e., we are goingto put them in the base as ATmProp, where m means “now”. The reader can find more detailsof this language in [CA99a].3 Motivation for a negation extensionThe definition of EMTPL includes the operator ¬, this operator can be part of a clause, morespecifically it can form part of the body of an EMTPL clause. We have previously seen that thesemantic of ¬ operator is:(σ, j) |= ¬p iff (σ, j) 6|= pIntuitively this is the negation as failure semantic, because it means that some formula ¬A istrue if and only if the system can not prove the truth of A. This semantic is quite differentfrom the classical negation semantic, in which the truth of ¬A depends only in the proof of thenegated formula. The decision of which semantic choose is quite important, because no matterwhich one the language support, it causes some effects on it. If we choose negation as failure,the system looses some properties of the underlying logic and a considerable set of theorems.Another disadvantage of this way of conceive negation is the restriction to manipulate negativeinformation. That means that we can not have in the base any negative information, this canbe seen in the fact that the negation operator can be only part of a body clause and that bodymust be proven in the system. On the other hand since databases are usually systems withincomplete information, classical negation will not always has an positive or negative answer13+φ =Def ∃n 3+n φ22+φ =Def ∀n 3+n φ3Workshop de Investigadores en Ciencias de la Computación WICC 2002Página 2689to all possible queries. Instead the system could answer true, false and unknown. In thedevelopment of EMTPL we though of critical data bases where the answer unknown is quitedangerous.Considering this we can think in the possibility of adding a new negation operator to EMTPLlanguage, i.e. the language keep having negation as failure, but provides some kind of temporalnegation, that allows manage negative information.3.1 Extension 1: EMTPL∇EMTPL∇ is like EMTPL, except for the new operator ∇. The syntax of the new languageEMTPL∇ is as follows:φ = p|¬φ|φ1 ∧ φ2|ATnφ|∇φ|3+n φ|∃n 3+n φ|∀n 3+n φ|3−n φ|∃n 3−n φ|∀n 3−n φAssuming a temporal structure like EMTPL’s one, the semantic of the new operator is:(σ, j) |= ∇p iff ∇p ∈ σ(j) or (σ, j) |= ¬pThe intuitive meaning of this semantic is: “∇p is true only if we have ∇p in the set of provenfacts, or we can not prove p” In order to avoid the or-problems of logic programming we onlyare going to allow the negation of atomic formulas.As a consequence of the definition we have the following definition of EMTPL∇Definition 2 (EMTPL∇)Let us consider a language with propositional atoms, the logic connectives: ∧,∨ →, ¬, ∇ andthe temporal operators: 3+n, 3−n, 3+, 3−, 2+, 2−. We define the notion of EMTP∇’s program, clause,always clause, ordinary clause, head, body and goal as follows:• A program is a set of “clauses”.• A clause is ATiC or C where C is an “ordinary clause”.• An ordinary clause is a “head” or a B → H , where B is a “body” and H is a “head”.• An atomic formula is an atom or ∇A where A is an atom.• A head is an atomic formula, 3+n A or 3−n A or 2+A or 2−A where A is a conjunction of“ordinary clauses”.• A body is an atomic formula, a conjunction of bodies, 3+n B or 3−n B or 2+A or 2−A or ¬Bwhere B is a body.• A goal is ATnB or B where B is any body or a disjunction of bodies.For example we can now infer negative information like in the following rule:in way(Car, Street)∧move(Car) → ∇free way(Street)In EMTPL, the previous rule is not allowed because it is meaningless to infer something whosevalue depends on the failure of some other proof. Also, we can consider a short example wherethe use of ∇ is different form ¬.op move(Car) ∧ in way(Car, Street2)∧ lateral way(Street, Street2) → free way(Street)In the previous rule if there are negative information the meaning change if we replace op with¬ or with ∇. That is because it is not the same infer that a car is not moving because we justknow that the car is not moving.4Workshop de Investigadores en Ciencias de la Computación WICC 2002Página 269703.2 Extension 2: EMTPL∇cThe new operator could be used as the realization operand AT or like 3+c but for negativeinformation. In this sense we can analyze what happens with an operator of this kind.The syntax of the language is quite similar to the corresponding to EMTPL∇ the onlymodification is that we replace ∇p by ∇c pLet see the semantic of ∇c, again we assume a temporal structure like EMTPL’s one.(σ, j) |= ∇c p iff (σ, j + c) |= ¬pWith this semantic we do not manage negative information in the same way as in 3.1, becausethe manipulation of that kind of information is, in some way, virtual.We can think in having both operators, but it seems to be not very attractive because alfirst sight we can think that:∇c p = 3+c∇pAlthough it can be interesting to analyze what happen with this kind of operators more carefully.4 Conclusions and future workWe show some ways of extend the language EMTPL to manage negative information. The ideabehind the first one is to combine classical negation and negation as failure, so we can havenegative information and also keep a two-valuate system. For this alternative we believe thatcan be interesting to find a way to make the operator∇ more flexible, i.e., analyze what happenswith the system if we extend its application to any formula instead of only atomic ones Theidea of the second extension is to provide some kind of temporal negation, this can lead to someinteresting operator.In both cases it should be analyzed how this extensions affects the expressiveness of thelanguage, and at the same take a look to the underlying logic part. Another aspect to consideris how to introduce these operators in an interpreter of our language.References[CA99a] Mar´ıa Laura Cobo and Juan Carlos Augusto. EMTPL: A Pogramming Language forTemporal Deductive Data Bases. In Proceedings de la XIX International Conference ofthe Chilean Computer Science Society, pages 170–178, Talca, Chile, 1999.[CA99b] Mar´ıa Laura Cobo and Juan Carlos Augusto. Fundamentos lo´gicos e implementacio´nde una extensio´n a temporal prolog. The Journal of Computer Science and Technol-ogy (JCS&T), sponsored by ISTEC (Iberoamerican Science & Technology EducationConsortium, 1(2):22–36, 1999.[CA00] Mar´ıa Laura Cobo and Juan Carlos Augusto. Towards a Programming Language Basedon Prior’s Metric Temporal Operators. In Proceedings del VI Congreso Argentino deCs. de la Computacio´n, CACiC2000, pages 453 –464, 2000.[Gab87] Dov Gabbay. Modal and temporal logic programming. In Antony Galton, editor,Temporal Logic and their Applications, pages 197–236. Academic Press, 1987.[Pri67a] Arthur Prior. Past, Present and Future. Clarendon Press, 1967.[Pri67b] Arthur Prior. Stratified metric tense logic. Theoria 33, pages 28–38, 1967.[RU71] Nicholas Rescher and Alasdair Urquhart. Temporal Logic. Springer-Verlag, 1971.5Workshop de Investigadores en Ciencias de la Computación WICC 2002Página 2701

An extension to EMTPL

http://sedici.unlp.edu.ar/bitstream/handle/10915/21891/Documento_completo.pdf?sequence=1

An extension to EMTPL

Abstract

Similar works

Full text

Available Versions

Servicio de Difusión de la Creación Intelectual