Costantini, S., Lanzarone, G.A.: A metalogic programming language. In Levi, G., Martelli, M., eds.: Proc. 6th Intl. Conf. on Logic Programming, Cambridge, Mass., The MIT Press (1989) 218--233  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by taxonomy, i.e, generalizing the query in case of an insufficient answer. In our own work [2; 3] we have taken this approach further allowing (in principle) arbitrary nonstandard inference rules kept in order by constraints on the proof produced by the prove predicate. Reflective Prolog [12] is a proposal for a programming language that integrates this programming by modifying the semantics style, making clear the reflections between the object and meta layers that take place. In [13] this framework is extended with a notion of metalevel negation which makes it possible to ....

Costantini, S., Lanzarone, G.A., A metalogic programming language, Logic Programming: Proc. of the Sixth International Conference, pp. 133--145, MIT Press, 1989.

....architecture can deal with temporal information. The proof procedure (IFF proof procedure [9] treats both inputs from the environment and agents actions as abducibles (hypotheses) Barklund et al. 1] and Costantini et al. 6] present an extension to the Re ective Prolog programming paradigm [7, 8] to model agents that are introspective and that communicate with each other. We will refer to this approach as Re ective Prolog with Communication (RPC) In RPC introspection is achieved via the meta predicate solve and communication is achieved via the meta predicates tell and told. A ....

....Integrity constraints provide a mechanism not only for constraining explanations and plans, for example, as in I 1 , but also for allowing reactive, conditionaction type of behaviour, for example, as in I 2 . 4 Re ective Prolog with communication 4. 1 Re ective Prolog Re ective Prolog (RP) [7, 8] is a metalogic programming language that extends the language of Horn clauses [11, 15] to include higher order like features. The language is that of Horn clauses except that terms are de ned di erently in order to include names that are intended to represent at the meta level the expressions of ....

[Article contains additional citation context not shown here]

S. Costantini and G. A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc. 6th Intl. Conf. on Logic Programming, pages 218{ 33, Cambridge, Mass., 1989. MIT Press.

.... have been advocated, e.g. 4, 11, 24] Representing and reasoning about object level theories is an important field in logic and artificial intelligence and has led to the development of logic languages that facilitate metaprogramming (e.g. the logic languages Godel [15] Reflective Prolog [6], Prolog [20] Our goal is to lay the foundations for a multi level metaprogramming environment that fully addresses the unique requirements of multi level program hierarchies and to develop techniques for efficient computation on all levels of a metasystem hierarchy. The present work addresses ....

S. Costantini and G. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proceedings Sixth International Conference on Logic Programming, pages 218--233. MIT Press, 1989.

....can be found in various textbooks on logic programming. Several workshop proceedings contain papers addressing theoretical problems related to meta programming [AR89, Met92] Logic programming languages based on the ideas of meta programming such as Godel [HL91] Hilog [CKW93] Reflexive Prolog [CL89] among others are beginning to gain ground in logic programming community. In this paper we will not even attempt to mention all directions of research related to meta programming. Instead we consider a few simple (but important) meta programs and try to outline several fundamental points related ....

S. Costantini and G.A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc ICLP'89, pages 218--233, 1989.

....a number of researchers and the semantics is now better understood. The other solution is for the programmer to write meta programs that use the ground representation. To save the user the work of constructing a ground representation, systems such as Godel (Hill Lloyd 1994) and Reflective Prolog (Costantini Lanzarone 1989) that provide a built in ground representation have been developed. There are advantages and disadvantages with each of these solutions. It is much more difficult to provide an efficient implementation when using the ground representation compared to the non ground representation. However, the ....

....variables, quantified over the terms of the object language. Note that, as the trivial naming relation is built into Prolog, the representation is trivially determined by means of an inference rule. However, there is no check that dte is ground before applying the inference rule. Reflective Prolog (Costantini Lanzarone 1989) (see below) is an example of a language with a non trivial naming relation, but where the representation and re representation are determined by inference rules. If a re representation was defined functionally, the meta program would require a function such as ReRepresent=1. Thus, for each ....

[Article contains additional citation context not shown here]

Costantini, S. & Lanzarone, G. (1989), A metalogic programming language, in G. Levi & M. Martelli, eds, `Sixth International Conference on Logic Programming, Lisbon', MIT Press, pp. 218--233.

....architecture can deal with temporal information. The proof procedure (IFF proof procedure [13] treats both inputs from the environment and agents actions as abducibles (hypotheses) Barklund et al. 1] and Costantini et al. 7] present an extension to the Reflective Prolog programming paradigm [8,9] to model agents that are introspective and that communicate with each other. We will refer to this approach as Reflective Prolog with Communication (RPC) In RPC introspection is achieved via the meta predicate solve and communication is achieved via the meta predicates tell and told. A ....

....Integrity constraints provide a mechanism not only for constraining explanations and plans, for example, as in I 1 , but also for allowing reactive, conditionaction type of behaviour, for example, as in I 2 . 4. Reflective Prolog with communication 4.1. Reflective Prolog Reflective Prolog (RP) [8,9] is a metalogic programming language that extends the language of Horn clauses [15,20] to include higher order like features. The language is that of Horn clauses except that terms are defined differently in order to include names that are intended to represent at the meta level the expressions of ....

[Article contains additional citation context not shown here]

S. Costantini and G. A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc. 6th Intl. Conf. on Logic Programming, pages 218--33, Cambridge, Mass., 1989. MIT Press.

....of ai systems with a meta level architecture have implemented a naming relation in the sense described above. For example, the Socrates knowledge representation system [8] directly implements a quotation mark naming relation, whereas the logic programming systems Godel [6] and Reflective Prolog [3] implement a structural descriptive naming relation 3 Naming Relations Should Be Definable In all systems described in the literature (with the possible exception of FOL, but see Sect. 8 for more discussion on this system) the naming relation has been attributed an external status: In ....

S. Costantini and G.A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proceedings of the Sixth International Conference on Logic Programming, pages 218--233, Lisbon, 1989. The MIT Press.

....5 and 7. Log does not supply any built in reflection operator which would allow a metarepresentation to be obtained from the object it denotes or vice versa. Neither it is possible to define such an operator using Log. This differentiates Log from other proposals, such as Reflective Prolog [CoL89] and R Prolog [Sug90] that, on the contrary, assume a reflection mechanism to be available (even though not visible at the user level) In Log meta levels are strictly separated: at each level, the syntactic entities of the lower levels are visible through their names only; variables do not ....

....Only when really needed it is then possible to access the structure of terms composing the given clause using the = operator. This differentiates our proposal by many other proposals which use a structural meta representation similar to that proposed by Barklund (e.g. Reflective Prolog [CoL89]) These proposals usually do not cover equally well the 18 naming of all the syntactic entities of the language, usually excluding the two extremes, namely programs and symbols. Indeed, having the structural representation only, may result quite cumbersome for the user representing programs ....

[Article contains additional citation context not shown here]

Costantini S., Lanzarone G.A.: "A Metalogic Programming Language", in Logic Programming - Proc. of the 6th International Conference (G. Levi, M. Martelli, Eds), MIT Press, 1989.

....to occur and interact in an intuitively appealing way. ffl One proof system allows a correct and efficient interleaving of computations at different metalevels, also in the presence of names of expressions with variables. The language has been influenced by Prolog [15] Reflective Prolog [18] and unnamed languages proposed by Kowalski [22, 23] The intended procedural semantics is an extension of that proposed by Barklund, Costantini, Dell Acqua and Lanzarone [4] The procedural semantics will be realized through translation to sequences of instructions for an abstract machine, ....

....The names pF (A; u)q and pF (A; v)q do not unify because that would imply puq = pvq , which is false. 4 Examples Before explaining the proof system of the language we shall look at two examples that show some of its abilities. The following program (from a similar Reflective Prolog program [18]) contains three theories denoted by the symbols M , O 1 and O 2 , where M is intended to be a metatheory of O 1 and O 2 . M pO 2 x( a; b)q pO 1 x( a; b)q (1) M pO 2 x( b; a)q Symmetric(x) pO 1 x( a; b)q (2) M Symmetric(pAs good asq) 3) O 1 As good as(p; ....

[Article contains additional citation context not shown here]

Costantini, S. and Lanzarone, G. A., A Metalogic Programming Language, in: G. Levi and M. Martelli (eds.), Proc. 6th Intl. Conf. on Logic Programming, MIT Press, Cambridge, Mass., 1989.

....can be found in various textbooks on logic programming. Several workshop proceedings contain papers addressing theoretical problems related to meta programming [AR89, Met92] Logic programming languages based on the ideas of meta programming such as Godel [HL91] Hilog [CKW93] Reflexive Prolog [CL89] among others are beginning to gain ground in logic programming community. In this paper we will not even attempt to mention all directions of research related to meta programming. Instead we consider a few simple (but important) meta programs and try to outline several fundamental points related ....

S. Costantini and G.A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc ICLP'89, pages 218--233, 1989.

....The MetaProlog compiler is able to compile theories also when they are only partially given. A preliminary declarative and operational semantics for MetaProlog was given by Subrahmanian [83] 5. 3 Reflective Prolog Reflective Prolog, which has been developed at Universit a degli Studi di Milano [20], allows the programmer to extend the object level provability relation by clauses to be used at the metalevel. However, a Reflective Prolog program is an amalgamated theory, containing object level axioms as well as metalevel axioms. For example, the clauses solve(#P( X, Y) reflexive(#P) ....

....engineering in the future. Given a language with metalevel capabilities, object level) programs could be specified implicitly through metalevel information, for example, in the form of metalevel programs. Such ideas have been put forward by, e.g. Kwok Sergot [56] Costantini Lanzarone [20], and Barklund Hamfelt [6] Other Forms of Program Manipulation. There are certainly many other kinds of metaprograms with a purpose to manipulate representations of programs, e.g. compilation, program synthesis, program verification, debugging, etc. We shall not elaborate on these kinds of ....

Costantini, S. and Lanzarone, G. A., A Metalogic Programming Language, in: G. Levi and M. Martelli (eds.), Proc. 6th Intl. Conf. on Logic Programming, MIT Press, Cambridge, Mass., 1989.

....noteworthy in this respect for committing to typed versions of the Vanilla meta interpreter. It is interesting to observe how most of these extensions loose the ease of programming medium granularity meta interpreter, although they improve the logical reading of finer granularity meta interpreters [1, 3, 4]. 3 The Linear Logic Programming Lolli Miller et al. 13] have defined a general criterion (the existence of uniform proofs) for extracting fragments of logical systems suited to be implemented as logic programming languages. The language of Horn clauses, on which Prolog is based, has been proven ....

S. Costantini, G.A Lanzarone.: "A Metalogic Programming Language.", in "Proceedings of the Sixth International Conference on Logic Programming" (G. Levi, M. Martelli, Eds), pp 218233, MIT Press, 1989.

....by the PROLOG representation of programs by means of the primitive relation clause. According to the theory [6,18] object level formulas (clauses) should be represented as metalevel data (ground terms) This choice, taken also in the design of new logic languages oriented towards metaprogramming [10,19], affects the granularity [32] of metainterpreters, leading to metaprograms which are both more complex (unification has to be redefined ) and less efficient. Even if the PROLOG non ground representation can be understood in terms of the ideas discussed by Richards [29] whose language handles ....

S. Costantini and G. A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc. Sixth Int'l Conf. on Logic Programming, pages 218--233. The MIT Press, Cambridge, Mass., 1989.

....considerably. 5. There is an SLD resolution style inference rule instead of an inference rule for program clauses. It should be obvious for the knowledgeable reader that the development of Alloy is very much inspired by work of Kowalski [25, 26] and by Reflective Prolog of Costantini Lanzarone [16]. There have recently appeared some proposals for systems for meta reasoning with a similar philosophy as ours. Attardi Simi [1] use what they call relativized truth but obtain a system quite similar to ours. One significant difference is that they choose to duplicate their inference system (a ....

Costantini, S. and Lanzarone, G. A., A Metalogic Programming Language, in: G. Levi and M. Martelli (eds.), Proc. 6th Intl. Conf. on Logic Programming, MIT Press, Cambridge, Mass., 1989.

.... A L B and A L B Th M Demo(A 0 ; B 0 ) A reflective system which respects these particularities is said to be an amalgamating language [Bow82] Dem94] Some reflective systems have been created in a way that they could be called amalgamating systems: metaProlog [Bow85] Reflective Prolog [CL89] and the different 3 Prolog languages [Dem94] 2 . These systems are concerned mainly with the representation of the predicate Demo presented earlier. However all these amalgamating systems are relatively inefficient (because of the meta programming techniques they use) For this reason, some ....

....be reflective because they contain in their definition some explicit use of upward and downward reflection which are specific predicates creating causal connection and access to reflective structures. This is the case of the languages CPU and ALPES IProlog. Only one language (Reflective Prolog [CL89] uses an implicit reflective mechanism which is made by defining reflective operations as metalevel definitions and taking care of reflective calls by an extended resolution procedure. 3.2.3 Reification and reflection The last issue most important for reflective languages is causal connection. ....

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S. Costantini and G. A. Lanzarone. A metalogic programming language. In Proc. of the 6th Int. Conference in Logic Prog. Workshop, 1989.

....be enough for the majority of meta programming applications in logic programming. No built in reflection mechanism, instead, is assumed to be available in Log, neither it is possible to program it using Log. This substantially differentiates Log from other proposals, such as Reflective Prolog [5] and R Prolog [16] that incorporate a reflection mechanism. In Log meta levels are strictly separated: at each level, the syntactic entities of the lower levels are visible through their names only. A distinguishing feature of Log is its naming scheme. Each Log syntactic entity has, in ....

Costantini S., Lanzarone G.A., "A Metalogic Programming Language.", in Proceedings of the Sixth International Conference on Logic Programming (G. Levi, M. Martelli, Eds), MIT Press, pp. 218-233, 1989.

....programs is problematic. 2. Another approach is to design a new logic programming language for the specific purpose of meta programming in the ground representation, with a specialized semantics for dealing with unification (and resolution) at the object and meta levels. This is the approach of [24, 6]. These languages, in particular Godel [24] require a large library of built in operations (such as substitution) There are also no known attempts to extend these experiments beyond first order Horn clauses (which are insufficient for higher order abstract syntax) Furthermore, these ....

S. Costantini and G. A. Lanzarone. A metalogic programming language. In Sixth International Conference on Logic Programming, pages 218--233. MIT Press, 1990.

....architecture can deal with temporal information. The proof procedure (IFF proof procedure [9] treats both inputs from the environment and agents actions as abducibles (hypotheses) Barklund et al. 1] and Costantini et al. 6] present an extension to the Reflective Prolog programming paradigm [7, 8] to model agents that are introspective and that communicate with each other. We will refer to this approach as Reflective Prolog with Communication (RPC) In RPC introspection is achieved via To appear as LNAI, Springer Verlag. c flSpringer Verlag. the meta predicate solve and communication ....

....Integrity constraints provide a mechanism not only for constraining explanations and plans, for example, as in I 1 , but also for allowing reactive, conditionaction type of behaviour, for example, as in I 2 . 4 Reflective Prolog with communication 4. 1 Reflective Prolog Reflective Prolog (RP) [7, 8] is a metalogic programming language that extends the language of Horn clauses [11, 15] to include higher order like features. The language is that of Horn clauses except that terms are defined differently in order to include names that are intended to represent at the meta level the expressions ....

[Article contains additional citation context not shown here]

S. Costantini and G. A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc. 6th Intl. Conf. on Logic Programming, pages 218-- 33, Cambridge, Mass., 1989. MIT Press.

No context found.

Costantini, S., Lanzarone, G.A.: A metalogic programming language. In Levi, G., Martelli, M., eds.: Proc. 6th Intl. Conf. on Logic Programming, Cambridge, Mass., The MIT Press (1989) 218--233

....on some form of metainterpretation) With explicit reflection and inefficient metalevel computation, metalevel knowledge will most often play a secondary role w.r.t. object level knowledge. To overcome these problems, a different concept of reflection has been incorporated into Reflective Prolog [19, 22], a self referential Horn clause language with logical reflection. The objective of this approach was that of developing a more expressive and 7 powerful language, while preserving the essential features of logic programming: Horn clause syntax, model theoretic semantics, resolution via ....

....of the reflection principle U (Reflection up) of Section 6.1, with demo instead of solve. Finally, let us review how the present paper relates to our own previous work on the matter. A language for building reflective, non conservative extensions of Horn clause theories was first proposed in [22] and fully defined formally in [24] The system was then augmented with a reflective, non monotonic negation apt to represent non monotonic reasoning [23] A formalization of analogical reasoning in this reflective logic was elaborated in [25] Reflection was used to represent communication among ....

S. Costantini and G. A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc. 6th Intl. Conf. on Logic Programming, pages 218--233, Cambridge, Mass., 1989. MIT Press.

.... the plain Horn clause language, but possibly in all its variations and extensions which are mainly based on variations and extensions of the classical semantics [13] One of these extensions is the metalogic programming language Re ective Prolog (for short RP) previously developed by the authors [1], 3] It is in fact immediate to obtain Re ective Prolog with analogy, which further enlarges the range of applicability. It provides, for free, declarative representation and use of metaknowledge and a declarative treatment of negation in analogy. The latter issue has never been considered ....

....versions of P s and P t , i.e. the (possibly in nite) programs obtained by instantiating every variable in each program in all possible ways over ground terms of its Herbrand universe. Declarative semantics of replacement based analogy will be de ned by applying the concepts introduced in [1], 3] 5] where it is shown that many extensions to the Horn clause language can be modeled with very limited modi cations to the standard semantics. This is obtained by implicitly augmenting a program with a denumerable set of new axioms, characterized by an axiom schema AX called a Re ection ....

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S. Costantini and G. A. Lanzarone, A Metalogic Programming Language, in Logic Programming, Proceedings of the Sixth International Conference, G. Levi and M. Martelli eds., The MIT Press, Cambridge (Mass.), 1989, 218-233.

....behave more rationally and flexibly towards users. Our argumentation will consist of a collection of examples of how to express different forms of interaction with a DKB by using a first order logic language with metalogical extensions. In particular, we refer to the language Reflective Prolog [Costantini, Lanzarone, 1989, Costantini, Lanzarone, 1994] We will try METAREASONING AGENTS FOR QUERY ANSWERING SYSTEMS 3 to show how the metalogical capabilities allow us to achieve various modalities of interaction, even though in principle they could be achieved using only object level language. This is similar to the ....

....axiom: A :solve( 0 A) It asserts that whenever an atom of the form solve( 0 A) is provable at the metaevaluation level of a theory , then A is provable at the object level of itself. Reflection axioms make the extensions of the language effective both semantically and procedurally [Costantini, Lanzarone, 1989]. Semantically, this has been achieved by introducing the notion of reflective model and reflective logical consequence [Costantini, 1990] Reflective models are models in the usual sense. For a logic program P without solve not clauses the model intersection property still holds, and therefore ....

Costantini, S., Lanzarone, G.A. A metalogic programming language. In: Levi, G., and Martelli, M., editors, Proc. 6th Intl. Conf. on Logic Programming, 218--33, Cambridge, Mass., 1989. MIT Press.

.... the most general form, this communication provides full visibility of the object level on the metalevel, while the policy of knowledge interchange from the metalevel to the object level can change, from no visibility (e.g. in Prolog metainterpreters) to full visibility (e.g. in Reflective Prolog [9, 10]) The dynamic communication of knowledge between levels has usually been called reflection. It can be explicit (if it is specified in the program) or, more generally, implicit (if conditions for communications are specified in the definition of the proof theoretical device) Previously, we have ....

Costantini, S. and Lanzarone, G. A., A Metalogic Programming Language, in: G. Levi and M. Martelli (eds.), Proc. 6th Intl. Conf. on Logic Programming, MIT Press, Cambridge, Mass., 1989.

....extensions The examples in this paper are written in two similar extensions of Horn clause logic. The example of Section 5 is expressed in Alloy [3, 4] a language designed for specifying systems of interrelated theories. The examples of Sections 3 and 4 are written in Reflective Prolog [6, 7]. Alloy Syntactically we can characterize the Alloy language as follows: ffl A program consists of a set of statements on the form or 1 j 2 , where each , 1 or 2 is a theory term and each is a program clause. A statement expresses that belongs to the theory while a ....

....Instead, by using a metaevaluation clause we can formalise our statement as solve(P ( 0 a) belongs to(P; class) where P is a metavariable ranging over the names of predicate symbols. Last, a form of logic reflection which makes this extensions effective both semantically and procedurally [6]. Semantically, this has been achieved by introducing the notion of reflective models. They are models in usual sense but satisfy an additional requirement that an atom A belongs to the model if and only if the atom solve( 0 A) belongs to the model. Procedural semantics of Reflective Prolog ....

Stefania Costantini and Gaetano A. Lanzarone. A metalogic programming language. In G. Levi and M. Martelli, editors, Proc. 6th Intl. Conf. on Logic Programming, pages 218--33, Cambridge, Mass., 1989. MIT Press.

....a schema than a specific language, because it admits many choices of naming strategies and also a variety of techniques for rewriting equalities involving names. For example, we can choose a naming relation and a rewrite system for names to obtain a slightly modified variant of Reflective Prolog [9, 10]. The question of using ground or nonground representations in metalogic programming has been discussed intensively for a long time. In this proposal we sidestep the question, as the proposed inference system restricts reflection so only ground expressions are ever communicated between levels. ....

Costantini, S. and Lanzarone, G. A., A Metalogic Programming Language, in: G. Levi and M. Martelli (eds.), Proc. 6th Intl. Conf. on Logic Programming, MIT Press, Cambridge, Mass., 1989.

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