L. Fari~nas del Cerro. MOLOG: A System that extends Prolog with Modal Logic. New Generation Computing, 4(1):35--50, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the formalisms which allow knowledge to be represented in a structured way, supporting more sophisticate reasoning mechanisms. Modal logics are one of the most appreciated and studied of such tools [37] On one hand, modal logics are useful to extend logic programming languages with new features [23, 27, 4, 3, 6]. On the other, they extend the classical framework by allowing the user to tackle in a pretty natural and task oriented way problems that require some form of distributed reasoning [47] One possible application of distributed reasoning is the construction of teams of agents, each of which has ....

L. Fari nas del Cerro. MOLOG: A System that extends Prolog with Modal Logic. New Generation Computing, 4(1):35--50, 1986.

....to prove soundness and completeness of the operational semantics with respect to model theoretic 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 proof procedure, fixpoint semantics and the notion of minimal Herbrand model. In this paper we ....

....proving the two subgoals htiG 1 and htiG 2 . For this reason, the policy of recording in a context Gamma the sequence of modalities that are found in front of a goal does not work in that case in a straightforward way. The class of languages we have presented has strong similarities with MOLOG [9], which is an extension of Prolog with modal operators. In MOLOG modalities may occur in front of clauses, in front of clause heads, and in front of goals. MOLOG can be regarded as a framework, which can be instantiated with particular modal logics. In [9] a resolution procedure, close to Prolog ....

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L. Fari~nas del Cerro. Molog: A system that extends Prolog with modal logic. New Generation Computing, (4):35--50, 1986.

....Keywords: Multimodal Logic, Embedded Implication, Translation. 1 Introduction Modal logics are widely used in computer science and artificial intelligence to deal with knowledge and beliefs, time, actions, and several researchers have proposed modal extensions of logic programming languages [7, 1, 13, 19, 17, 6]. In particular, in [5] we have defined a modal logic programming language which allows both multiple modalities and embedded implications. The language has been shown to be well suited for structuring knowledge, and, in particular, for defining module constructs within programs, for representing ....

L. Fari~nas del Cerro. Molog: A system that extends Prolog with modal logic. New Generation Computing, (4):35--50, 1986.

....knowledge operator. In this language we can also define modules, compose them in several ways, and, also, we can perform hypothetical reasoning. 1 Introduction The problem of extending logic programming languages with modal operators, has been studied by several researchers. In particular, in [4] an extension of Prolog with modal operators, called MOLOG, is proposed, and a resolution procedure, close to Prolog resolution, is defined for modal Horn clauses in the logic S5 which contain universal modal operators of the form Know(a) Another modal extension of logic programming is the ....

L. Fari~nas del Cerro. Molog: A system that extends Prolog with modal logic. New Generation Computing, (4):35--50, 1986.

....0 1 : L 0 m ) we can have a resolvent [ i ] L 1 : Lm L 0 1 : L 0 m ) The key point in positional resolution is that: Two clauses can be resolved if they have the same positional modal context. Positional resolution principle is similar to modal resolution principle of [4] to some extent. Following the ideas of first order temporal tableau and transitional tableau rules of [16] we can also develop positional tableau rules for positional operators when we always keep in mind that a set of formulas appear in the same tableau if they are in the same positional modal ....

L. Fari~nas del Cerro, MOLOG: A system that extends PROLOG with modal logic, New Generation Computing 35--50, 1986.

....are viewed as worlds, with more or less explicit parallels drawn to the possible worlds semantics of modal logics. From among the merger systems, mentioned in Section 2.1, Prolog KR, Mandala and CPU take this approach. From proper modal extensions of Prolog, we mention MULTILOG [KG86] and MOLOG [Far86]. In OO applications of the modal logic paradigm, the accessibility relation between worlds correlates with the isa relation. Sorting relies on many sorted logics. Plain many sorted logics offer no relation between sorts. To provide a counterpart for subtype supertype (i.e. isa) relation, ....

L. Fariņas del Cerro. MOLOG: A system that extends Prolog with modal logic. New Gener. Computing, 4(1):35-50, 1986.

....in Section 5) cannot be defined. The language we have presented differs form most of other proposals of extending logic programming with modal and temporal operators in that it allows hypothetical implications to occur in goals. In particular, this makes the language different from MOLOG [14], which is an extension of Prolog with modal operators. In MOLOG modalities may occur in front of clauses, in front of clause heads, and in front of goals. MOLOG can be regarded as a framework, which can be instantiated with particular modal logics. In [14] a resolution procedure, close to Prolog ....

....makes the language different from MOLOG [14] which is an extension of Prolog with modal operators. In MOLOG modalities may occur in front of clauses, in front of clause heads, and in front of goals. MOLOG can be regarded as a framework, which can be instantiated with particular modal logics. In [14] a resolution procedure, close to Prolog resolution, is defined for modal Horn clauses in the logic S5 which contains only universal modal operators of the form Know(a) In [3] a modal SLD resolution method is presented for a fragment of MOLOG in which 2 is disallowed in the bodies of modal ....

L. Fari~nas del Cerro. Molog: A system that extends Prolog with modal logic. New Generation Computing, (4):35--50, 1986.

.... are based on linear time temporal logic; Temporal Prolog [15] is based on linear and branching time temporal logic; InTense [23, 24] is based on a multi dimensional logic with multiple spatial and temporal dimensions; MTL [10] is based on a temporal logic with metric and past operators; and Molog [13] is based on modal logic. For more details, we refer the reader to the surveys of Fisher and Owens [14] and Orgun and Ma [27] Just as the logics these languages are based on, their execution mechanisms differ markedly in the way programs are interpreted and answers to queries are obtained. In ....

....into a sequence of state descriptions over an interval that satisfies the original program [25, 16] Templog [3] Temporal Prolog [15] and Chronolog [28, 31] are extensions of logic programming in which programs are executed to obtain answers by the use of resolution type proof procedures. Molog [13] uses modal inference rules, and a resolution type proof procedure. Tokio [4] is based on the same interval logic as Tempura, but its execution mechanism is a mixture of transformation and resolution. There are also several attempts at developing the declarative and operational semantics for these ....

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Luis Fari~nas del Cerro. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing, 4:35--50, 1986.

....represents the residue list [2,3,5] at time 1, meaning that the second Hamming number is 2. At time 2, by the third clause, 2 is removed from the residue list and multiples of 2 are merged with the rest of the residue list (the list [3,5] The residue predicate represents the residue list [3,4,5,6,10] at time 2, meaning that the third Hamming number is 3. The computation proceeds along these lines. The open ended goal clause hamming(N) triggers a non terminating computation of Hamming numbers. The goal is interpreted as an infinite series of canonical sub goals into the future of the form ....

....notion of a state is captured within the module. 4 Conclusions We have introduced the temporal logic language Chronolog(Z) and outlined its features. Other applications of non classical logics to logic programming include the multi dimensional language InTense [11] and the modal framework Molog [6]. For more details on temporal and modal logic programming, we refer the reader to the literature; for example, see [7] We believe that these non classical languages will open up new application areas for logic programming. ....

L. Fari~nas del Cerro. Molog: A system that extends prolog with modal logic. New Generation Computing, 4:35--50, 1986.

....encapsulation. A concrete implementation of the ideas is Prolog [MN86] The proof search procedure can be found in [Nad93] Hodas and Miller [HM91] refined this approach for linear intuitionistic logic. Beside these, a number of different LP languages based on modal logics have been proposed, e.g. [Far86]. 3 Structural Synthesis of Programs (SSP) Structural synthesis of programs as put forth by Mints and Tyugu is an approach to synthesis of functional programs in a deductive fashion from specifications stated as types. The specification method employed in SSP is based on using types as ....

Luis Fari~nas del Cerro. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing, 4(1):35--50, 1986.

....of non classical logics to logic programming include the interval languages Tokio [3] and Tempura [27] and the multi dimensional language InTense [26] which has an arbitrary number of temporal and spatial dimensions. InTense restricted to a time dimension is very similar to Chronolog(Z) Molog [11] is a framework for modal logic programming in which a specific modal resolution method is required for each particular modal logic used. Jackson and Reichgelt [19] gives a more general proof method for modal predicate logic which can also be applied to Molog. Brzoska [8] showed that Templog can ....

L. Fari~nas del Cerro. Molog: A system that extends prolog with modal logic. New Generation Computing, 4:35--50, 1986.

....Even more, if the current goal contains enough information to produce the next goal, or if we just want to simplify a goal or to reorder literals we don t need to select a fact clause at all. The assumptions (1) and (2) were at base of the development of a meta level inference system called MOLOG [FdC86] ABFdC 86] BFdCH88] Esp87b] Esp87a] The inference machine that is presented in this paper is a complete rewriting of MOLOG realizing assumption (4) It has been developped at IRIT ( Bri87] and [AG88] A formal specification of the inference mechanism called TIM : Toulouse Inference ....

L. Fari~nas del Cerro. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing, 4:35--50, 1986.

....and modal logic programming languages: In Tempura [13, 10] programs are systematically transformed into a sequence of state descriptions over an interval that satisfies the original program Templog [2] Temporal Prolog [9] and Chronolog [15] are temporal extensions of logic programming. Molog [8] uses modal inference rules, and a resolution type proof procedure. Tokio [3] is based on the same interval logic as Tempura, but its execution mechanism is a mixture of transformation and resolution. There are also several attempts at developing the declarative and operational semantics for these ....

Luis Fari~nas del Cerro. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing, 4:35--50, 1986.

.... 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 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 approaches to temporal and modal logic programming [7, 36] Some other non classical extensions of ....

....that the accessibility relations be reflexive, transitive, symmetric or antisymmetric, etc. Depending on the properties of the accessibility relations (or the corresponding set of axioms) we have a different modal logic. We first discuss three modal logic programming languages (or schemes) Molog [39] (which has evolved into TIM [14, 15] Modal Prolog [87] and Akama s proposal of modal logic programming [6] In these works, some traditional modal logics such as B, D, S4, S5 and so on are considered, and proof procedures specialized for these modal logics are proposed. There are also ....

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Luis Fari~nas del Cerro. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing, 4:35--50, 1986.

....be freely mixed in methods which both return information and have side effects. So it is not by chance that the attempts to use DL for OOLP has come from the formal specification community and not from the logic programming community. Also, there are quite a few LP systems implementing modal logic [27, 29], and they are more theorem provers than programming systems. 5 Perpetual Objects: Exploiting the Dynamics of Proofs As was mentioned in the introductory section, the notion of truth in classical logic is global and static. However there is a dynamic component in a LP or automated proof system: ....

L. Fari~nas del Cerro. MoLog: A system that extends Prolog with modal logic. New Generation Computing, 4(1):35--50, 1986.

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L. Fari~nas del Cerro. MOLOG: A System that extends Prolog with Modal Logic. New Generation Computing, 4(1):35--50, 1986.

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