D. Miller: "A logical analysis of modules in logic programming", in Journal of Logic Programming, Vol. 6, 1989, pp 79-108.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....context D # above (# #) is empty, and so we introduce P into a subproof where G is the only goal. Logical modularity and locality underlie the use of the proof theory of modal logic as a declarative framework for structuring specifications, and thereby facilitating their design and reuse [Miller, 1989, Giordano and Martelli, 1994, Baldoni et al. 1993, Baldoni et al. 1996, Baldoni et al. 1998a] Concretely, a goal that specifies the part of the program to be used in its proof will give rise to the same operational behavior when other parts of the program change. In this paper, I further ....

....Moreover, such fragments make it more difficult to enforce modularity as well, since they do not permit an eigenvariable condition at (# #) inferences in goal directed proofs. My investigation therefore sticks closely to the treatments of logical modularity and locality originally explored in [Miller, 1989, Giordano and Martelli, 1994] Indeed, I continue to restrict implications and universal quantifiers in goals to strict statements of the form G) and ##xG. The basic strategy that I adopt is to start with a relatively straightforward proof system, and gradually to narrow the formulation of its ....

Miller, D. (1989). A logical analysis of modules in logic programming. Journal of Logic Programming, 6(1--2):79--108.

....operator r behaves identically on and . From this, it follows that P and P c have the same classes of proper models, which implies the theorem. 2 5.2 Proof Rules In this section we develop a goal directed sequent style proof system for ORLog programs. We adopt this style along the lines of [21, 22]. In Figure 5 below, we present four inference rules which de ne the properties of the proof predicate . We use the notation P c G to represent the fact that the goal G is derivable from the closed program P c with a substitution , i.e. P c G . Following [22] the structure of the ....

....the empty goal, which is always true. Our proof theory consists of four inference rules empty, and, deduction and inheritance. For the sake of clarity, we present the rst three inference rules rst and explain their intuition and our conventions. Then, we present the last inference rule. As in [21], a proof for P c G is a tree rooted at P c G with internal nodes that are instances of one of the four inference rules and with the leaf nodes that are labelled with the gure empty. The height of a proof is the maximum of the number of nodes in all the branches in the proof tree, and the ....

D. Miller. A Logical Analysis of Modules in Logic Programming. Journal of Logic Programming, 6(1/2):79-108, January/March 1989.

....right as to the head. With respect to standard Horn logic syntax, the main novelty in the definitions above is that we permit implications in goals and in the bodies of definite clauses. Extended Horn logic syntax of this kind has been proposed to implement hypothetical reasoning [3] and modules [7] in logic programming. We shall first make clear the use of this extension for the purpose of linguistic description, and we shall then illustrate its operational meaning. 3 First order Categorial Grammar 3.1 Definite Clauses as Types We take CONN (for connects ) to be a threeplace predicate ....

....and at the same time provides the ability to account for constructions which, as shown in section 3.3.1, are problematic for an (albeit specialized) proposi tional framework. 4. 1 An Intuitionistic Exterision of Prolog The inference system we are going to introduce below has been proposed in [7] as an extension of Prolog suitable for modular logic programming. A similar extension has been proposed in [3] to implement hypotethical reasoning in logic program ming. We are thus dealing with what can be con sidered the specification of a general purpose logic programming language. The ....

[Article contains additional citation context not shown here]

Miller, Dale. 1987. A Logical Analysis of Mod- ules in Logic Programming. To appear in the Journal of Logic Programming.

....It is natural to want to have access to the structure of these models. 4. 5 Logic Programming BI gives rise to a notion of logic programming which builds in a sharing interpretation of BI s connectives [38, 41, 42, 37, 2] Our underlying notion of logic programming is that introduced in [33, 32], based on the sequent calculus. Programs, P , and goals, G, are modelled by the left and right hand sides, respectively, of sequents P G; read as, Is there an instance of G which is a consequence of P In BI, programs are bunches of formul, consisting of data, or facts , and ....

.... L; with , atomic and [t=x] t=x] often, is retained in the left hand premiss) In intuitionistic logic, simple uniform proofs, which are goal directed and in which the non determinism is confined to the choice of implicational formula, are complete for hereditary Harrop sequents [33, 32]. In general, G contains what Prolog calls logical variables , which are existentially quantified, and we seek substitution instances of G which are consequences of P . 21 Simple, uniform proofs amount to the analytic notion of resolution. In BI, the corresponding class of sequents may be ....

[Article contains additional citation context not shown here]

D. Miller. A logical analysis of modules in logic programming. J. Logic. Programming, 6(1& 2):431--483, 1981. 38

....It is natural to want to have access to the structure of these models. 4. 5 Logic Programming BI gives rise to a notion of logic programming which builds in a sharing interpretation of BI s connectives [39, 42, 43, 38, 2] 21 Our underlying notion of logic programming is that introduced in [34, 33], based on the sequent calculus. Programs, P , and goals, G, are modelled by the left and right hand sides, respectively, of sequents P G; read as, Is there an instance of G which is a consequence of P In BI, programs are bunches of formul, consisting of data, or facts , and ....

.... L; with , atomic and [t=x] t=x] often, is retained in the left hand premiss) In intuitionistic logic, simple uniform proofs, which are goal directed and in which the non determinism is confined to the choice of implicational formula, are complete for hereditary Harrop sequents [34, 33]. Simple, uniform proofs amount to the analytic notion of resolution. In BI, the corresponding class of sequents may be defined. Bunched hereditary Harrop formul are given by the following grammar, in which A denotes atoms (we simplify a bit, for brevity) Definite formul D : A j D D j G A ....

[Article contains additional citation context not shown here]

D. Miller. A logical analysis of modules in logic programming. J. Logic. Programming, 6(1& 2):431--483, 1981.

....any theorems for the restricted class of Horn Theories and existential goals. This approach to completeness has had a remarkable success in logic programming: countless extensions of declarative programming to e.g. constraints [30] abstract interpretation [5, 11] Hereditarily Harrop programming [44], higher order logic [17, 18] build on a similar completeness proof. We take this semantic definition as a foundation for a categorical treatment of uniform logic programming. A slight change in the presentation of the Kowalski van Eraden semantics is more consistent with the spirit of categorical ....

Dale Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, pages 79-108, 1989.

....2 INDEFINITE INFORMATION 1 Overview Like all programming languages, logic programming languages need structuring constructs to describe the modularity of programs and thereby to facilitate their design and reuse. Modal logic provides a declarative setting to develop such structuring constructs [Miller, 1989, Giordano and Martelli, 1994, Baldoni et al. 1993, Baldoni et al. 1996] A necessary goal 2G can be seen as a modular goal because, in modal logic, only program clauses of the form 2P can contribute to its proof. With the right modal semantics, modularity also brings locality: a goal 2(P ....

Miller, D. (1989). A logical analysis of modules in logic programming. Journal of Logic Programming, 6(1--2):79--108.

....fragments of HOHH (see [22, 3] based on work by Henkin [13] and Andrews [1] on the semantics of Church s classical Type theory [6] Nadathur s dissertation [20] provides a notion of term model for the HOHH fragment. Miller de nes a Kripke like bottom up semantics for a rst order fragment [15] in which the syntax of programs is built into the notion of model. In A semantics for Prolog , D.A. Wolfram [22] provided semantics for the classical higherorder Horn clause fragment of Prolog, a result which was independently established in Bai and Blair [3] and was built on work in ....

....considered here requires intuitionistic logic and, consequently, an intuitionistic model theory. Until recently (see [8, 9] no such semantics had been developed even for the intuitionistic Church s type theory of which HOHH is an executable fragment. Operationality: bottom up semantics In [15], Miller produced an indexed variant of Kripke style models for a rst order fragment of lambda Prolog in which the conventional de nition of truth in Kripke semantics at a possible world p in an arbitrary poset: p A B i for every q p; q A ) q B (1) 1 The notion of an abstract ....

[Article contains additional citation context not shown here]

Dale Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, pages 79-108, 1989.

....of a unique stable model. All these proposals, however, despite of their differences, deal with overriding on a per predicate basis and do not consider any form of state evolution 6 . A finer granularity of rule composition is offered by languages supporting embedded implication [BGM96,Fre92,Mil89] Embedded implication allows one to realize also some of the other features of our language (such as message passing and conservative inheritance) but does not account for all of them (for instance, overriding) We remark, moreover, that our way of supporting such features is very closely ....

D. Miller. A Logical Analysis of Modules in Logic Programming. Journal of Logic Programming, 6(1-2):79--108, 1989.

....(i.e. G ) Possible applications of Prolog are chiefly the applications that motivated the introduction of terms [45, 40] manipulation of formulas, computation of denotations, etc. see Section 4. 1) Notice also that the structure of Prolog encompasses such constructions as modules [37] and abstract data types [35] without any extralogical addition. There have been actual applications of Prolog for automatic theorem proving [4, 20] analysis of natural and formal languages [48, 14, 28, 55] the manipulation of functional programs [23] and the specification of digital circuits ....

....constructed with the implication connective (i.e. D ) 2 ftp: alonzo.tip.cs.cmu.edu afs cs project ergo export ess 3 ftp: ftp.irisa.fr local pm . 4 Philip Wickline at University of Pennsylvania 5 http: www.cis.upenn.edu dale lProlog index.html 3 discusses the connections with modules [37], abstract data types [35] and abstract syntax [34] In the same group, Felty investigates the connection with theorem proving [21] There exist, however, global presentations of, or related to, Prolog that we will compare with our reconstruction in the final discussion. To ease the way of a ....

D.A. Miller. A logical analysis of modules in logic programming. J. Logic Programming, 6(1--2):79--108, 1989.

....this in Section 2.1.4) Possible applications of Prolog are chiefly the applications that motivated the introduction of terms [46, 40] manipulation of formulas, computation of denotations, etc. see Section 3. 1) Notice also that the structure of Prolog encompasses such constructions as modules [35] and abstract data types [33] without any extralogical additions. There have been actual applications of Prolog for automatic theorem proving [3, 15] analysis of natural and formal languages [52, 11, 28, 56] and the manipulation of functional programs [21] Note also applications which mix ....

....requirement that justifies the whole of Prolog. In the beginning, Miller and Nadathur present a logic programming language called Prolog, which features higher order Horn clauses, terms, and equivalence [40, 46] Then, Miller formalizes module importation as logical implication in goals, G [35], and module abstraction as universal quantification in goals, 8 G [33] Miller et al. observe that these extensions form a well behaved fragment of intuitionistic logic [43, 42] This fragment is called hereditary Harrop formulas, and the extended language is still called Prolog. Table 1.1 ....

[Article contains additional citation context not shown here]

D.A. Miller. A logical analysis of modules in logic programming. J. Logic Programming, 6(1--2):79--108, 1989.

....and their computation may be identified as searching for proofs: given a program P and a goal G we attempt to satisfy G by searching for a proof of P G using the inference rules of a given logic. There have been various proof theoretic approaches to the design of logic programming languages [1, 2, 5, 7, 12, 16, 21] and a corresponding variety of languages implemented (Prolog [24] Lolli[12] LinLog[1] Prolog[20] Forum[18] Lygon[26] among others) However, despite many similarities in such analyses, the issue of a criterion for the identification of logic programming languages remains problematic. The ....

....in question, and which are common to previously analysed systems. In addition, it should be noted that the completeness of goal directed proofs, whilst important, is not generally sufficient; often further properties are imposed on proofs. A common such property is requiring proofs to be simple [16], i.e. all occurrences of the left implication rule must have the right hand premise being an axiom. As discussed and analysed in [27] there are a number of other such properties of proofs which desirable in a logic programming system (such as the existential property, lack of contraction in ....

Miller D. A logical analysis of modules in logic programming, Journal of Logic Programming 6:79-108, 1989.

....only to prove G 1 . In [Mil89] Miller has shown how implications can be used to structure logic programs into modules. Universal quanti cation allows the creation of fresh names during the execution of a goal. This idea has been used, e.g. to implement hiding mechanism for module systems [Mil89,Mil89b]. To sum up, proving that a formula G is a logical consequence of a program P in intuitionistic logic, amounts to search for a goal driven proof of P G. This can be done automatically in the incomplete theorem prover Prolog [NM88] In fact, Prolog implements a left to right selection rule of ....

D. Miller. A Logical Analysis of Modules in Logic Programming. JLP 6(1&2): 79-108, 1989.

No context found.

Miller, D. A logical analysis of modules in logic programming. Journal of Logic Programming 6 (1989) 79 -- 108.

....modus ponens and cut elimination. This situation improves a bit if intuitionistic logic is used instead: the notion of truth in Kripke models involving possible worlds allows for some richer modeling of dynamics, enough, for example, to provide direct for scoping of modules and abstract datatypes [Mil89b,Mil89a]. If one selects a substructural logic, such as linear logic, for encoding logic programs, then greater encoding of computational dynamics is possible. In linear logic, for example, it is possible to model a switch that is now on but later o# and to assign and update imperative programming like ....

Dale Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, 6(1-2):79--108, January 1989.

No context found.

D. Miller: "A logical analysis of modules in logic programming", in Journal of Logic Programming, Vol. 6, 1989, pp 79-108.

No context found.

Dale Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, 6(1-2):57--77, January 1989.

No context found.

Dale Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, 6(1--2):79--108, 1989.

No context found.

Dale Miller. A logical analysis of modules in logic programming. The Journal of Logic Programming, 6(1 and 2):79--108, January/March 1989.

No context found.

D. Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, pages 79-108, 1989.

No context found.

D. Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, pages 79-108, 1989.

No context found.

D. Miller. A logical analysis of modules in Logic Programming. J. Logic Programming, 1989:79--108.

No context found.

D. Miller. A logical analysis of modules in logic programming. Journal of Logic Programming, 6:79--108, 1989.

No context found.

D. Miller. A Logical Analysis of Modules in Logic Programming. Journal of Logic Programming, 6(2):79--108, 1989.

No context found.

D. Miller, "A logical Analysis of Modules in Logic Programming," Journal of Logic Programming vol. 6, nos. 1& 2 (1989) pp. 79-108.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC