Efficient determinization of visibly and height-deterministic pushdown automata

New algorithms for the determinization of nondeterministic visibly and nondeterministic real-time height-deterministic pushdown automata are presented. The algorithms improve the results of existing algorithms. They construct only accessible states and necessary pushdown symbols of the resulting deterministic pushdown automata.     

Propositional dynamic logic of context-free programs and fixpoint logic with chop

This paper compares propositional dynamic logic of non-regular programs and fixpoint logic with chop. It identifies a fragment of the latter which is equi-expressive to the former. This relationship transfers several decidability and complexity results between the two logics.     

A dynamic logic of action

The paper presents a logical treatment of actions based on dynamic logic. This approach makes it possible to reflect clearly the differences between static and dynamic elements of the world, a distinction which seems crucial to us for a representation of actions.Starting from propositional dynamic logic a formal system (DLA) is developed, the programs of which are used to model action types. Some special features of this system are: Basic aspects of time are incorporated in DLA as far as they are needed for our purpose. Names for states and for instants are simulated by formulas. It is possible to express formally that a formula is satisfiable or valid. A special program is introduced to reflect developments which are not caused by an official agent but by external influences.Having presented our basic system DLA we give some examples to illustrate how a logical system of this kind could be used for analysing essential aspects of actions. We therefore touch on such topics asthe results of actions, abilities of the agent, parallel performances of actions. Possibilities of and problems with logical representations of these features are informally discussed. Afterwards first steps towards integrating them into our basic systems are proposed by formally presenting an extension of DLA for each of the topics mentioned. Statement of exclusive submission. This paper has not been submitted elsewhere in identical or similar form.     

一种模糊动态描述逻辑

分析了目前描述逻辑DL的研究现状和存在的问题,特别是动态描述逻辑DDL作为语义Web逻辑基础所存在的问题。针对语义Web需要处理模糊和不精确知识的特点和需求,对DDL进行了模糊化扩充,提出了一种新的描述逻辑,即模糊动态描述逻辑FDDL。给出了FDDL的语法和语义,研究了FDDL的推理机制。与动态描述逻辑DDL相比,该FDDL可以为语义Web提供更为合理的逻辑基础,弥补了DDL作为语义Web逻辑基础的不足。     

Propositional semantics for disjunctive logic programs

In this paper we study the properties of the class of head-cycle-free extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NP-completeness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion.     

基于命题逻辑的关联规则挖掘算法L-Eclat

关联规则挖掘是数据挖掘领域非常重要的课题,在很多领域被广泛应用。关联规则挖掘算法都需要设置最小支持度和最小置信度。很多国内外学者研究的挖掘算法在这两方面都存在着一些问题,不仅需要大量的领域知识来设置合适的最小支持度,而且其结果集庞大、用户不容易理解。针对关联规则挖掘算法存在的问题,将命题逻辑融合到关联规则算法Eclat中,设计出了基于命题逻辑思想的挖掘算法L-Eclat。实验结果表明,L-Eclat算法压缩了挖掘的规则集,减小了算法的时间消耗,且即使是非常小的支持度也可以得到高质量的关联规则,这在一定程度上解决了支持度设置的问题。     

Linearizing some recursive logic programs

We give a sufficient condition under which the least fixpoint of the equation X=a+f(X)X equals the least fixpoint of the equation X=a+f(a)X. We then apply that condition to recursive logic programs containing chain rules: we translate it into a sufficient condition under which a recursive logic program containing n⩾2 recursive calls in the bodies of the rules is equivalent to a linear program containing at most one recursive call in the bodies of the rules. We conclude with a discussion comparing our condition with the other approaches to linearization studied in the literature     

The word problem for visibly pushdown languages described by grammars

Visibly pushdown languages are an interesting subclass of deterministic context-free languages that can model nonregular properties of interest in program analysis. Such class properly contains typical classes of parenthesized languages such as “parenthesis”, “bracketed”, “balanced” and “input-driven” languages. It is closed under boolean operations and has decidable decision problems such as emptiness, inclusion and universality. We study the membership problem for visibly pushdown languages, and show that it can be solved in time linear in both the size of the input grammar and the length of the input word. The algorithm relies on a reduction to the reachability problem for game graphs. We also discuss the time complexity of the membership problem for the class of balanced languages which is the largest among those cited above. Besides the intrinsic theoretical interest, we further motivate our main result showing an application to the validation of XML documents against Schema and Document Type Definitions (DTDs). Work partially supported by funds for the research from MIUR 2006, grant “Metodi Formali per la verifica di sistemi chiusi ed aperti”, Università di Salerno. A preliminary version of this paper was published in the Proceedings of the 4th International Symposium Automated Technology for Verification and Analysis (ATVA 2006), Lecture Notes in Computer Science 4218, pp. 96–109, 2006.     

Composing recursive logic programs withClausal join

A family of methods for composing logic programs from simpler components is presented. Specifically, simple pairs of programs operating on lists, trees and other recursive structures are composed to generate a single program with composite functionality. The methods are based onclausal join, a specific sequence of unfold/fold transformations for deriving a new clause from a given pair of clauses and a join specification.Procedural join composes a new procedure from two given procedures by applyingclausal join to all pairs of their clauses.1-1 Join composes a new procedure from closely related procedures by applyingclausal join to corresponding pairs only.Meta join is a modification of1-1 join for composing meta-interpreters. The transformations are straightforward to implement in Prolog, as is demonstrated in the paper.     

Branch-and-cut solution of inference problems in propositional logic

We describe and test computationally a branch-and-cut algorithm for solving inference problems in propositional logic. The problem is written as an integer program whose variables correspond to atomic propositions. We generate cuts for the integer program using a separation algorithm based on the resolution method for theorem proving. We find that the algorithm substantially reduces the size of the search tree when it is large. It is faster than Jeroslow and Wang's method on hard problems and slower on easy problems.Supported in part by the US Air Force Office of Scientific Research, grant AFOSR-87-0292.     

Rewriting of visibly pushdown languages for XML data integration

In this work, we focus on XML data integration by studying rewritings of XML target schemas in terms of source schemas. Rewriting is very important in data integration systems where the system is asked to find and assemble XML documents from the data sources and produce documents that satisfy a target schema.As schema representation, we consider Visibly Pushdown Automata (VPAs), which accept Visibly Pushdown Languages (VPLs). The latter have been shown to coincide with the family of (word-encoded) regular tree languages, which are the basis of formalisms for specifying XML schemas. Furthermore, practical semi-formal XML schema specifications (defined by simple pattern conditions on XML) compile into VPAs that are exponentially more concise than other representations based on tree automata.Notably, VPLs enjoy a “well-behavedness” that facilitates us in addressing rewriting problems for XML data integration. Based on VPAs, we positively solve these problems, and present detailed complexity analyses.     

Equivalent logic programs and symmetric homogeneous forms of logic programs with equality

This article introduces the notion of CAS-equivalent logic programs: logic programs with identical correct answer substitutions. It is shown that the notions CAS-equivalence, refutational equivalence, and logical equivalence do not coincide in the case of definite clause logic programs. Least model criteria for refutational and CAS-equivalence are suggested and their correctness is proved. The least model approach is illustrated by two proofs of CAS-equivalence. It is shown that the symmetric extension of a logic program subsumes the symmetry axiom and the symmetric homogeneous form of a logic program with equality subsumes the symmetry, transitivity, and predicate substitutivity axioms of equality. These results contribute towards the goal of building equality into standard Prolog without introducing additional inference rules.     

一种采用一阶动态逻辑表示的数字权限描述模型

针对已有数字权限描述模型的动态语义描述能力较弱问题,提出了一个能够描述权限动 作状态的数字产品权限描述模型DDRM。基于一阶动态逻辑,定义了一个用于描述数字权限概念的 一阶动态逻辑符号系统DrFDL,并在DDRM模型基础上给出了DrFDL的语义结构(该语义结构能够 反映动作的动态特性)。基于DDRM模型还给出了一个表达权限证书的文法,应用DrFDL逻辑语言 给出了该文法生成的权限证书的形式语义,并探讨了该证书的确定性和有效性。     

On the structure of graphs in the Caucal hierarchy

We investigate the structure of graphs in the Caucal hierarchy. We provide criteria concerning the degree of vertices or the length of paths which can be used to show that a given graph does not belong to a certain level of this hierarchy. Each graph in the Caucal hierarchy corresponds to the configuration graph of some higher-order pushdown automaton. The main part of the paper consists of a study of such configuration graphs. We provide tools to decompose and reassemble their runs, and we prove a pumping lemma for higher-order pushdown automata.     

Mathematical logic and quantum finite state automata

This paper is a review of the connection between formulas of logic and quantum finite-state automata in respect to the language recognition and acceptance probability of quantum finite-state automata. As is well known, logic has had a great impact on classical computation, it is promising to study the relation between quantum finite-state automata and mathematical logic. After a brief introduction to the connection between classical computation and logic, the required background of the logic and quantum finite-state automata is provided and the results of the connection between quantum finite-state automata and logic are presented.     

Most specific logic programs

More specific versions of definite logic programs are introduced. These are versions of a program in which each clause is further instantiated or removed and which have an equivalent set of successful derivations to those of the original program, but a possibly increased set of finitely failed goals. They are better than the original program because failure in a non-successful derivation may be detected more quickly. Furthermore, information about allowed variable bindings which is hidden in the original program may be made explicit in a more specific version of it. This allows better static analysis of the program's properties and may reveal errors in the original program. A program may have several more specific versions but there is always a most specific version which is unique up to variable renaming. Methods to calculate more specific versions are given and it is characterized when they give the most specific version.     

Redundancy in logic I: CNF propositional formulae

A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study some problems related to the redundancy of a CNF formula. In particular, any CNF formula can be made irredundant by deleting some of its clauses: what results is an irredundant equivalent subset. We study the complexity of problems related to irredundant equivalent subsets: verification, checking existence of an irredundant equivalent subset with a given size, checking necessary and possible presence of clauses in irredundant equivalent subsets, and uniqueness. We also consider the problem of redundancy with different definitions of equivalence.     

基于逻辑证书的数字权利动态描述模型研究*

数字权利的动态描述一直都是DRM应用系统研究的热点。提出了一种基于逻辑证书的数字权利的动态描述模型。在定义好相关的逻辑证书和逻辑规则后,利用逻辑推理的方法深入探讨和分析该模型中数字证书逻辑推理过程,通过逻辑推理的方法实现数字权利的动态描述。最后通过简单实例,验证了该方法的可行性。