121.
Extension of WAM for a linear-logic-based logic programming language
- Yukio Kaneda; Naoyuki Tamura; Naoyuki Tamura
This paper describes an extension of WAM instruction set for a logic programming language called LLP which is based on intuitionisic linear logic. LLP includes additive and multiplicative conjunction, linear implication in a goal, exponential (!) for atomic resource formula, and the constant 1. The extension of WAM is mainly for efficient resource management: especially for resource look-up and deletion. In our design, only one table is maintained to keep resources during the execution. Looking-up of a resource is done through a symbol table or a hash table. Deletion of a resource is done by just "marking" the entry in...
122.
The Complexity of Fuzzy Logic
- Goldstern, Martin
Lukasiewicz logic is a "fuzzy" logic in which truth value can be real numbers
in the unit interval. There are connectives for min, max, addition and
complement (1-x). The "value" of a closed formula in a fuzzy (relational
model) is defined in the natural way.
A formula is called valid iff it has value 1 in every fuzzy model.
We show that the set of valid formulas in Lukasiewicz predicate logic is a
complete Pi^0_2 set.
We also show that if we restrict our attention to the classical language
(min, max, complement) then the classically valid formulas are exactly those
formulas whose fuzzy value is 1/2.
123.
Lógica dinámica con operadores ambiguos
- Artigas Prous, Josep
El almacenaje de Cooper es una técnica que ha sido desarrollada para tratar la ambigüedad semántica causada por el alcance de los cuantificadores. La Ambiguous Predicate Logic (APL) de van Eijck and Jaspars (1996) es una lógica ambigua que utiliza un método inspirado en esta técnica para formular representaciones subespecificadas. En esta comunicación proponemos equipar las teorías dinámicas de la semántica del lenguaje natural, en concreto la Dynamic Predicate Logic (DPL) de Groenendijk and Stokhof (1991), con el método de subespecificación de la APL. El resultado es una lógica dinámica subespecificada y propia.
124.
The logic of neural networks
- Trillas, Enric; Castro, J. L.
This paper establishes the equivalence between multilayer feedforward networks and linear combinations of Lukasiewicz propositions. In this sense, multilayer forward networks have a logic interpretation, which should permit to apply logical techniques in the neural networks framework.
125.
Modelling Digital Logic in SDL
- Tadanori Mizuno; Norio Shiratori; Teruo Higashino; G. Csopaki; K. J. Turner
The specification of digital logic in SDL (Specification and Description Language) is investigated. A specification approach is proposed for multi-level descriptions of hardware behaviour and structure. The modelling method exploits features introduced in SDL-92. The approach also deals with the specification, analysis and simulation of timing aspects at any level in the specification of digital logic. Keywords: Digital Logic, Hardware Design, SDL (Specification and Description Language), Timing Analysis. FORTE/PSTV Codes: I.1, I.3, I.4, I.7, I.8, I.9, II.3, IV.1. 1. Introduction 1.1 Application of SDL This paper addresses the specification and validation of digital logic components and digital systems using SDL-92...
126.
Combinators and Structurally Free Logic
- J. Michael Dunn; Robert K. Meyer
A "Kripke-style" semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the Routley-Meyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for "combinatory posets." A philosophical interpretation is given of the models, showing that an element of a combinatory poset can be understood simultaneously as a set of states and as a set of (untyped) actions on states. This double interpretation allows for one such element to be applied to another (including itself). Application turns out to be modeled the same...
127.
A Compiler System of a Linear Logic Programming Language
- Naoyuki Tamura; Yukio Kaneda
Linear logic developed by J.-Y. Girard can be described as a logic of resources. There have been several proposals for logic programming language based on linear logic: LO, LinLog, ACL, Lolli, Lygon, and Forum. Lolli and Lygon are implemented as interpreter systems (on SML and Prolog for Lolli, on Prolog for Lygon). But, none of them have been implemented as a compiler system. This paper describes a compiler system of a linear logic programming language called LLP. New features of LLP with various example programs are also shown. LLP is a superset of Prolog and a subset of Lolli. LLP...
128.
Linear Logic
- Patrick Lincoln
this paper we will restrict attention to propositional linear logic.
The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions,
and greek letters for sequences of formulas. A sequent is composed of two sequences of
formulas separated by a `, or turnstile symbol. One may read the sequent Delta ` Gamma as asserting
that the multiplicative conjunction of the formulas in Delta together imply the multiplicative
disjunction of the formulas in Gamma.
A sequent calculus proof rule consists of a set of hypothesis sequents, displayed above a
horizontal line, and a single conclusion sequent, displayed below the line, as below:
Hypothesis1 Hypothesis2
Conclusion
4 Connections to Other...
129.
Paraconsistent Declarative Semantics for Extended Logic Programs
- Ofer Arieli
We introduce a fixpoint semantics for logic programs with two kinds of negation:...
130.
A Compiler System of a Linear Logic Programming Language
- Naoyuki Tamura; Yukio Kaneda
Linear logic developed by J.-Y. Girard can be described as a logic of resources. There have been several proposals for logic programming language based on linear logic: LO, LinLog, ACL, Lolli, Lygon, and Forum. Lolli and Lygon are implemented as interpreter systems (on SML and #Prolog for Lolli, on Prolog for Lygon). But, none of them have been implemented as a compiler system.
131.
Lógica propedéutica y lógica teorética
- Bueno, Miguel
132.
Functional Reading of Logic Programs
Abstract: We propose an embedding of logic programming into lazy functional programming in which each predicate in a Prolog program becomes a Haskell function, in such a way that both the declarative and the procedural reading of the Prolog predicate are preserved. The embedding computes by means of operations on lazy lists. The state of each step in computation is passed on as a stream of answer substitutions, and all the logic operators of Prolog are implemented by explicit Haskell operators on these streams. The search strategy can be changed by altering the basic types of the embedding and the...
133.
Le Fun: Logic, equations, and Functions
- Hassan Aït-kaci; Patrick Lincoln; Roger Nasr
Abstract † We introduce a new paradigm for the integration of functional and logic programming. Unlike most current research, our approach is not based on extending unification to general-purpose equation solving. Rather, we propose a computation delaying mechanism called residuation. This allows a clear distinction between functional evaluation and logical deduction. The former is based on the λ-calculus, and the latter on Horn clause resolution. In clear contrast with equation-solving approaches, our model supports higher-order function evaluation and efficient compilation of both functional and logic programming expressions, without being plagued by non-deterministic term-rewriting. In addition, residuation lends itself naturally to...
134.
Operational Interpretations of Linear Logic
- David N. Turner; Philip Wadler
Two different operational interpretations of intuitionistic linear logic have been proposed in the literature. The simplest interpretation recomputes non-linear values every time they are required. It has good memory-management properties, but is often dismissed as being too inefficient. Alternatively, one can memoize the results of evaluating non-linear values. This avoids any recomputation, but has weaker memory-management properties. Using a novel combination of type-theoretic and operational techniques we give a concise formal comparison of the two interpretations. Moreover, we show that there is a subset of linear logic where the two operational interpretations coincide. In this subset, which is sufficiently expressive...
135.
Le Fun: Logic, equations, and Functions
- Hassan Ait-kaci; Patrick Lincoln; Roger Nasr
y We introduce a new paradigm for the integration of functional and logic programming. Unlike most current research, our approach is not based on extending unification to general-purpose equation solving. Rather, we propose a computation delaying mechanism called residuation. This allows a clear distinction between functional evaluation and logical deduction. The former is based on the -calculus, and the latter on Horn clause resolution. In clear contrast with equation-solving approaches, our model supports higher-order function evaluation and efficient compilation of both functional and logic programming expressions, without being plagued by non-deterministic term-rewriting. In addition, residuation lends itself naturally to process...
136.
Logic Programs with Ordered Disjunction
- Gerhard Brewka; Ilkka Niemelä; Tommi Syrjänen
Logic programs with ordered disjunction (LPODs) contain a new connective which allows representing alternative, ranked options for problem solutions in the heads of rules: A B intuitively means that if possible A, but if A is not possible, then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a...
137.
Super Logic Programs
- Stefan Brass; Jurgen Dix; Teodor C. Przymusinski
this paper, we specialize it to a class of theories called "super logic programs". We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas.
138.
A Theory of Logic Programming
In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Our framework captures several quite distinct logic programming semantics, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic...
139.
Fuzzy Logic -- from MathWorld
- Weisstein, Eric W.
An extension of two-valued logic such that statements need not be true or false, but may have a degree of truth between 0 and 1. Such a system can be extremely useful in designing control logic for real-world systems such as elevators. See also: Alethic, False, Logic, True
140.
A Strong Model of Paraconsistent Logic
- Esser, Olivier
The purpose of this paper is mainly to give a model of paraconsistent
logic satisfying the "Frege comprehension scheme" in which we can develop
standard set theory (and even much more as we shall see). This is the
continuation of the work of Hinnion and Libert.
