Results 1  10
of
46
A Tableau Calculus for Multimodal Logics and Some (Un)Decidability Results
 IN PROC. OF TABLEAUX98
, 1998
"... In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axio ..."
Abstract

Cited by 24 (8 self)
 Add to MetaCart
In this paper we present a prefixed analytic tableau calculus for a class of normal multimodal logics and we present some results about decidability and undecidability of this class. The class is characterized by axioms of the form [t 1 ] : : : [t n ]' oe [s1 ] : : : [sm ]', called inclusion axioms, where the t i 's and s j 's are constants. This class of logics, called grammar logics, was introduced for the first time by Farinas del Cerro and Penttonen to simulate the behaviour of grammars in modal logics, and includes some wellknown modal systems. The prefixed tableau method is used to prove the undecidability of modal systems based on unrestricted, context sensitive, and context free grammars. Moreover, we show that the class of modal logics, based on rightregular grammars, are decidable by means of the filtration methods, by defining an extension of the FischerLadner closure.
Implementing the Linear Logic Programming Language Lygon
 INTERNATIONAL LOGIC PROGRAMMING SYMPOSIUM
, 1995
"... There has been considerable work aimed at enhancing the expressiveness of logic programming languages. To this end logics other than classical first order logic have been considered, including intuitionistic, relevant, temporal, modal and linear logic. Girard's linear logic has formed the basis of a ..."
Abstract

Cited by 22 (8 self)
 Add to MetaCart
There has been considerable work aimed at enhancing the expressiveness of logic programming languages. To this end logics other than classical first order logic have been considered, including intuitionistic, relevant, temporal, modal and linear logic. Girard's linear logic has formed the basis of a number of logic programming languages. These languages are successful in enhancing the expressiveness of (pure) Prolog and have been shown to provide natural solutions to problems involving concurrency, natural language processing, database processing and various resource oriented problems. One of the richer linear logic programming languages is Lygon. In this paper we investigate the implementation of Lygon. Two significant problems that arise are the division of resources between subbranches of the proof and the selection of the formula to be decomposed. We present solutions to both of these problems.
A Framework for Modal Logic Programming
 In Joint International Conference and Symposium on Logic Programming
, 1996
"... In this paper we present a framework for developing modal extensions of logic programming, which are parametric with respect to the properties chosen for the modalities and which allow sequences of modalities of the form [t], where t is a term of the language, to occur in front of clauses, goals and ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
In this paper we present a framework for developing modal extensions of logic programming, which are parametric with respect to the properties chosen for the modalities and which allow sequences of modalities of the form [t], where t is a term of the language, to occur in front of clauses, goals and clause heads. The properties of modalities are specified by a set A of inclusion axioms of the form [t 1 ] : : : [t n ]ff oe [s 1 ] : : : [s m ]ff. The language can deal with many of the wellknown modal systems and several examples are provided. Due to its features, it is particularly suitable for performing epistemic reasoning, defining parametric and nested modules, describing inheritance in a hierarchy of classes and reasoning about actions. A goal directed proof procedure of the language is presented, which is modular with respect to the properties of modalities. Moreover, we define a fixpoint semantics, by generalizing the standard construction for Horn clauses, which is used to prov...
Transforming the .NET Intermediate Language Using Path Logic Programming
, 2002
"... Path logic programming is a modest extension of Prolog for the specification of program transformations. We give an informal introduction to this extension, and we show how it can be used in coding standard compiler optimisations, and also a number of obfuscating transformations. The object language ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
Path logic programming is a modest extension of Prolog for the specification of program transformations. We give an informal introduction to this extension, and we show how it can be used in coding standard compiler optimisations, and also a number of obfuscating transformations. The object language is the Microsoft .NET intermediate language (IL).
A Fixpoint Semantics and an SLDResolution Calculus for Modal Logic Programs
, 2001
"... We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLDresolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog program P ..."
Abstract

Cited by 15 (13 self)
 Add to MetaCart
We propose a modal logic programming language called MProlog, which is as expressive as the general modal Horn fragment. We give a fixpoint semantics and an SLDresolution calculus for MProlog in all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5, KD45, and S5. For an MProlog program P and for L being one of the mentioned logics, we define an operator TL,P, which has the least fixpoint IL,P. This fixpoint is a set of formulae, which may contain labeled forms of the modal operator ✸, and is called the least Lmodel generator of P. The standard model of IL,P is shown to be a least Lmodel of P. The SLDresolution calculus for MProlog is designed with a similar style as for classical logic programming. It is sound and complete. We also extend the calculus for MProlog in the almost serial modal logics KB, K 5, K 45, and KB5. 1
Multimodal Logic Programming and Its Applications to Modal Deductive Databases
, 2003
"... We give a general framework for developing the least model semantics, xpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rstorder Horn formulas. Our appr ..."
Abstract

Cited by 13 (9 self)
 Add to MetaCart
We give a general framework for developing the least model semantics, xpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rstorder Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems.
Beyond AOP: Toward Naturalistic Programming
 IN: OOPSLA'03 SPECIAL TRACK ON ONWARD! SEEKING NEW PARADIGMS & NEW THINKING (ACM
, 2003
"... Software understanding for documentation, maintenance or evolution is one of the longeststanding problems in Computer Science. The use of “highlevel” programming paradigms and objectoriented languages helps, but fundamentally remains far from solving the problem. Most programming languages and sy ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
Software understanding for documentation, maintenance or evolution is one of the longeststanding problems in Computer Science. The use of “highlevel” programming paradigms and objectoriented languages helps, but fundamentally remains far from solving the problem. Most programming languages and systems have fallen prey to the assumption that they are supposed to capture idealized models of computation inspired by deceptively simple metaphors such as objects and mathematical functions. Aspectoriented programming languages have made a significant breakthrough by noticing that, in many situations, humans think and describe in crosscutting terms. In this paper we suggest that the next breakthrough would require looking even closer to the way humans have been thinking and describing complex systems for thousand of years using natural languages. While natural languages themselves are not appropriate for programming, they contain a number of elements that make descriptions concise, effective and understandable. In particular, natural languages referentiality is a key factor in supporting powerful program organizations that can be easier understood by humans.
MultiDimensional Logic Programming
 Special Issue: Proc. of the 6th International Conf. on Computing and Information
, 1994
"... This paper introduces an extension of logic programming based on multidimensional logics. In a multidimensional logic the values of elements vary depending on more than one dimension, such as time and space. The resulting logic programming language is suitable for modelling objects which involve i ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
This paper introduces an extension of logic programming based on multidimensional logics. In a multidimensional logic the values of elements vary depending on more than one dimension, such as time and space. The resulting logic programming language is suitable for modelling objects which involve implicit and/or explicit temporal and spatial dependencies. The execution of programs of the language is based on a resolutiontype proof procedure called MSLDresolution. MSLDresolution is based on the axioms and rules of inference of the underlying multidimensional logic. Several example programs are given, including Conway's game of life. A spreadsheet interface to multidimensional logic programming is also outlined; it can be used as a powerful display tool with the advantage of nondeterminism inherent in logic programming. 1 Introduction Nonclassical logics such as temporal and modal logic have been successfully used as a formalism in many areas, including program specification and v...
Multimodal logic programming
 Theoretical Computer Science
, 2006
"... We give a framework for developing the least model semantics, fixpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ∀x ∃y Ri(x, y)) and some classical firstorder Horn formulas. Our approach is dir ..."
Abstract

Cited by 12 (7 self)
 Add to MetaCart
We give a framework for developing the least model semantics, fixpoint semantics, and SLDresolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ∀x ∃y Ri(x, y)) and some classical firstorder Horn formulas. Our approach is direct and no special restriction on occurrences of ✷i and ✸i is required. We apply our framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T, B, 4, 5 (in the form, e.g., 4: ✷iϕ → ✷j✷kϕ) and I: ✷iϕ → ✷jϕ. Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLDresolution calculi proposed for them are more efficient.
Evaluation of
 Behaviour and Information Technology
, 1981
"... We introduce pseudonaive evaluation, a method for execution of mixed topdown/bottomup logic programs and deductive databases. The method is intermediate in power between naive evaluation and seminaive evaluation. Pseudonaive evaluation adds a datadriven component to naive evaluation without ex ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
We introduce pseudonaive evaluation, a method for execution of mixed topdown/bottomup logic programs and deductive databases. The method is intermediate in power between naive evaluation and seminaive evaluation. Pseudonaive evaluation adds a datadriven component to naive evaluation without explicitly collecting the ‘delta ’ sets of new facts derivable at each iteration. Instead, it identifies certain body atoms as ‘triggers ’ and collects an abstraction of the delta sets, thereby simplifying the implementation. A rule is invoked only when new tuples for its trigger atoms are derived. Pseudonaive evaluation is most efficient on stronglystratified programs: programs for which all (positive and negative) bottomup recursion is mediated by an increasing temporal parameter. However, the method can still be used on programs with general recursion, by using either topdown calls, timestamped tuples to represent delta sets, or tupleatatime bottomup execution. A desirable feature enjoyed by our system is that it runs piggyback on most logic programming implementations, but performance is good because most of the code is compiled and executed by the native Prolog system. Proceedings of the Tenth Australasian Database Conference, Auckland, New Zealand, January 18–21 1999 Copyright SpringerVerlag, Singapore. Permission to copy this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or personal advantage; and this copyright notice, the title of the publication, and its date appear. Any other use or copying of this document requires specific prior permission from SpringerVerlag. 1 1