Logical Definition Research Articles

Description Logics and Planning

■ This article surveys previous work on combining planning techniques with expressive representations of knowledge in description logics to reason about tasks, plans, and goals. Description logics can reason about the logical definition of a class and automatically infer class-subclass subsumption relations as well as classify instances into classes based on their definitions. Descriptions of actions, plans, and goals can be exploited during plan generation, plan recognition, or plan evaluation. These techniques should be of interest to planning practitioners working on knowledge-rich application domains. Another emerging use of these techniques is the semantic web, where current ontology languages based on description logics need to be extended to reason about goals and capabilities for web services and agents.

Quantum logic as motivated by quantum computing

§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff and von Neumann introduced quantum logic in a seminal paper in 1936 [1]. But the definition of quantum logic varies among authors (see [2]). How to capture the logic structure inherent in quantum mechanics is very interesting and challenging. Given the close connection between classical logic and theoretical computer science as exemplified by the coincidence of computable functions through Turing machines, recursive function theory, and λ-calculus, we are interested in how to gain some insights about quantum logic from quantum computing. In this note we make some observations about quantum logic as motivated by quantum computing (see [5]) and hope more people will explore this connection.The quantum logic as envisioned by Birkhoff and von Neumann is based on the lattice of closed subspaces of a Hilbert space, usually an infinite dimensional one. The quantum logic of a fixed Hilbert space ℍ in this note is the variety of all the true equations with finitely many variables using the connectives meet, join and negation. Quantum computing is theoretically based on quantum systems with finite dimensional Hilbert spaces, especially the states space of a qubit ℂ2. (Actually the qubit is merely a convenience.

The new role of the corporate and functional strategies in the tourism sector: Spanish small and medium-sized hotels

This article aims at establishing the presence or lack of possible relationships between the existence of a logical global strategy definition in Spanish small and medium-sized hotels and its links with functional or department strategies involving four areas – marketing, technology, human resources and finance. Results show that there is a relationship between enterprise size – using business turnover as a yardstick – and the proper definition of technology, human resources and finance functions. There is also a relationship between enterprise size, determined by the number of employees, and an adequate definition of corporate strategy and technology and human resources department functions. A binding relationship has been found to exist between marketing and human resources department policies, between technology and finance policies, and lastly between the areas of human resources and finance. A relationship has also been established between strategies devised by enterprise management and policies conducted by marketing and technology departments.

Reconstructing Criticism: Pope’s Essay on Criticism and the Logic of Definition by Philip Smallwood

Reconstructing Criticism: Pope’s Essay on Criticism and the Logic of Definition by Philip Smallwood

フレーゲ論理哲学的探究の認識論的位相とメタ理論の可能性

First I will characterize Frege's "logicism" epistemologically. His "logicism" is originated from his epistemological claim of the "analyticity" of arithmetic. In order to confirm this, it needs to show that any arithmetic proposition is derivable from the logical laws with the logical definitions alone. Nevertheless there was no such powerful logic in the 19th century, and so Frege was forced to invent the radically new logic.Further Frege understands inferences and judgments epistemologically. He construes an inference as justifying a conclusion based on its premises, and both premises and conclusion as assertions/judgments, which Frege takes as holding true, whereas he regards the justified conclusion as recognition of its truth (knowledge).Frege's "sense" is not only the contribution to the truth-condition, but is also related to the cognitive value of a proposition, to the modes of presentation of the designation, and to various propositional attitudes, as is well known.Second I expound Fregean semantic explanations of logic, and mention Fregean meta-theoretic proof of independence briefly.

Thomas Pogge’s Global Resources Dividend: A Critique and an Alternative

AbstractPogge’s proposal for a Global Resources Dividend (GRD) has been criticized because its likely effects would be less predictable than Pogge supposes and could even be counterproductive to the main aim of relieving poverty. The GRD might also achieve little with respect to its secondary aim of promoting environmental protection. This article traces the problems to Pogge’s inadequate conception of natural resources. It proposes instead to conceive of natural resources in terms of ‘ecological space’. Using this conception, redistributive principles follow with a more definite logic from Pogge’s own supporting moral argument. The proposed alternative approach also promises a more direct contribution to Pogge’s secondary aim of resource conservation and environmental protection. I conclude that if any redistributive resource-based tax should be levied on nations, then there are at least four decisive reasons to favour levying a tax related to a nation’s per capita utilization of ecological space rather than the GRD.

Handling threats, rewards, and explanatory arguments in a unified setting

Current logic-based handling of arguments has mainly focused on explanation or justification-oriented purposes in presence of inconsistency. So only one type of argument has been considered, and several argumentation frameworks have then been proposed for generating and evaluating such arguments. However, recent works on argumentation-based negotiation have emphasized different other types of arguments such as threats, rewards, and appeals. The purpose of this article is to provide a logical setting that encompasses the classical argumentation-based framework and handles the new types of arguments. More precisely, we give the logical definitions of these arguments and their weighting systems. These definitions take into account that negotiation dialogues involve not only agents' beliefs (of various strengths), but also their goals (having maybe different priorities), as well as the beliefs on the goals of other agents. In other words, from the different beliefs and goals bases maintained by agents, all the possible threats, rewards, explanations, and appeals that are associated with them can be generated. It may also happen that an intended threat, or reward, is not perceived as such by the addressee and thus misses its target because the addresser misrepresents the addressee's goals. The proposed approach accounts for that phenomenon. Finally, we show how to evaluate conflicting arguments of different types. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1195–1218, 2005.

Conversation with Griffith Edwards

Conversation with Griffith Edwards

A geometric interpretation of LD-resolution

We devise an interpretation of a binarised definite logic program in a geometric framework which is closer to Dynamical Systems than to Logic. The building blocks of our framework are a family of affine sub-modules in a free finitely generated module over a special kind of ring. We describe SLD -resolution of definite binary programs as the iterated action of a finite union of affine graphs, associated to the program clauses, on a certain set of affine varieties associated to the original syntactic terms. This action is shown to faithfully represent the running of the corresponding program on a given goal, since all answers and only those answers the program would output are obtained. Hence, a programming language such as pure Prolog completely falls within our description.

An unfold/fold transformation framework for definite logic programs

Given a logic program P , an unfold/fold program transformation system derives a sequence of programs P = P 0 , P 1 , …, P n , such that P i +1 is derived from P i by application of either an unfolding or a folding step. Unfold/fold transformations have been widely used for improving program efficiency and for reasoning about programs. Unfolding corresponds to a resolution step and hence is semantics-preserving. Folding, which replaces an occurrence of the right hand side of a clause with its head, may on the other hand produce a semantically different program. Existing unfold/fold transformation systems for logic programs restrict the application of folding by placing (usually syntactic) conditions that are sufficient to guarantee the correctness of folding. These restrictions are often too strong, especially when the transformations are used for reasoning about programs. In this article we develop a transformation system (called SCOUT) for definite logic programs that is provably more powerful (in terms of transformation sequences allowed) than existing transformation systems. This extra power is needed for a novel use of logic program transformations: for the verification of a specific class of concurrent systems, called parameterized concurrent systems.Our transformation system is constructed by developing a framework, which is parameterized by a "measure space" and associated measure functions. This framework places no syntactic restriction on the application of folding, and it can be used to derive transformation systems (by fixing the measure space and functions). The power of the system is determined by the choice of the measure space and functions; thus the relative power of different transformation systems can be compared by considering their measure spaces and functions. The correctness of these transformation systems follows from the correctness of the framework. We show that various existing transformation systems can be obtained as instances of our framework. We extend the unfold/fold transformation framework with a goal replacement transformation that allows semantically equivalent conjunctions of atoms to be interchanged. We then derive a new transformation system SCOUT as an instance of the framework and show its power relative to the existing transformation systems. SCOUT has been used to inductively prove temporal properties of parameterized concurrent systems (infinite families of finite state concurrent systems). We demonstrate the use of the additional power of SCOUT in constructing such induction proofs.

A geometric interpretation of LD-resolution

We devise an interpretation of a binarised definite logic program in a geometric framework which is closer to Dynamical Systems than to Logic. The building blocks of our framework are a family of affine sub-modules in a free finitely generated module over a special kind of ring. We describe SLD-resolution of definite binary programs as the iterated action of a finite union of affine graphs, associated to the program clauses, on a certain set of affine varieties associated to the original syntactic terms. This action is shown to faithfully represent the running of the corresponding program on a given goal, since all answers and only those answers the program would output are obtained. Hence, a programming language such as pure Prolog completely falls within our description.

Fuzzy logic and nursing.

In empiricism, there are only two answers for a question: black or white. Yet, subjective meanings of human behaviours and responses toward health and illness cannot be simply explained with black and white. Gray zones are needed because they are characterized by complexity and require a contextual understanding. In this paper, we present and suggest fuzzy logic as an example of theoretical bases that help transcend the conflicts between objectivity and subjectivity, respect gray zones between black and white answers for questions, and provide a contextual understanding of complex nursing phenomenon. A historical review of fuzzy logic is followed by a definition of fuzzy logic. Then, fuzzy logic is discussed in terms of its compatibility with nursing epistemological views and philosophical thoughts. Fuzzy logic agrees with three categories of epistemological views of nursing, including correspondence, coherence and pragmatism. Fuzzy logic also agrees with four major philosophical thoughts in nursing, including postempiricism, pragmatism, feminism, and postmodernism. Based on the discussion, we propose that fuzzy logic be further explored, used and developed in research and practice in the nursing areas/situations/phenomena that are characterized by complexity, ambiguousness, and vagueness.

Recursion and corecursion have the same equational logic

This paper is concerned with the equational logic of definitions whose semantics is given in terms of final coalgebra maps. The framework for our study is iteration theories (cf. e.g. Bloom and Ésik, Iteration Theories: The Equational Logic of Iterative Processes, EATCS Monographs on Theoretical Computer Science, Springer, Berlin, 1993; Theoret. Comput. Sci. 179 (1–2) (1997)), recently re-introduced as models of the FLR 0 fragment of the formal language of recursion (Hurkens et al., J. Symbolic Logic 63 (2) (1998) 45; Mos Chovakis, J. Symbolic Logic 54 (1989) 1216; in: M.L. Dalla Chiara et al. (Eds.), Logic and Scientific Methods, Kluwer, Dordrecht, 1997, p. 179). We present a new class of iteration theories derived from final coalgebras. This allows us to reason with a number of types of fixed-point equations which heretofore seemed to require metric or order-theoretic ideas. All of the work can be done using finality properties and equational reasoning. Having a semantics, we obtain the following completeness result: the equations involving fixed-point terms which are valid for final coalgebra interpretations are exactly those valid in a number of contexts pertaining to recursion. For example, they coincide with the equations valid for least-fixed-point recursion on dcpo's. We also present a new version of the proof of the well-known completeness result for iteration theories (see Ésik, Comput. Linguistics Comput. Languages 4 (1982) 95; Hurkens et al., 1998). Our work brings out a connection between coalgebraic reasoning and recursion.

Proposal of Dynamic Process Resolution Protocol making transparency of physical locations in closed communication group for intranet

AbstractOn an intranet, there is a need to form various kinds of closed communication groups that protect significant information in departmental and/or individual bases. To satisfy this need, encryption elements realizing closed communication groups require exact and complicated process information in which the processes of how to treat the received packets are specified. In general, this information is generated in a management server and downloaded to the encryption elements. However, by this method, the information must be regenerated and redownloaded to the encryption elements, every time the system configuration changes. In this paper, we propose the Dynamic Process Resolution Protocol, by which encryption elements generate the process information automatically from the logical definition of the closed communication groups for themselves, detecting the relationship of the locations among the encryption elements and the communication terminals. This method means that the function of generation of process information is split from the management server. This method imposes no work on the network manager when the system configuration changes if the logical definition does not change. Moreover, closed communication groups with free location are realized, that is, users who have the function of encryption elements can move anywhere in the intranet freely. © 2002 Wiley Periodicals, Inc. Syst Comp Jpn, 34(1): 29–44, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1182

Revisiting quantification in autoepistemic logic

In this article, we introduce first-order autoepistemic logic. Our definition is semantical and is based on the intuition similar to that lying behind the definition of first-order default logic. Thus, our definition of first-order autoepistemic logic well complies with that of first-order default logic and circumscription, providing a substantial evidence for its acceptance.

Validating firewalls using flow logics

The ambient calculus is a calculus of computation that allows active processes to communicate and to move between sites. A site is said to be a protective firewall whenever it denies entry to all attackers not possessing the required passwords. We devise a computationally sound test for validating the protectiveness of a proposed firewall and show how to perform the test in polynomial time. The first step is the definition of a flow logic for analysing the flow of control in mobile ambients; it amounts to a syntax-directed specification of the acceptability of a control flow estimate. The second step is to define a hardest attacker and to determine whether or not there exists a control flow estimate that shows the inability of the hardest attacker to enter; if such an estimate exists, then none of the infinitely many attackers can enter unless they contain at least one of the passwords, and consequently the firewall cannot contain any trap doors.

DATA FLOW COHERENCE CONSTRAINTS FOR PRUNING THE SEARCH SPACE IN ILP TOOLS

In this paper we present a new method that uses data-flow coherence constraints in definite logic program generation. We outline three main advantages of these constraints supported by our results: i) drastically pruning the search space (around 90%), ii) reducing the set of positive examples and reducing or even removing the need for the set of negative examples, and iii) allowing the induction of predicates that are difficult or even impossible to generate by other methods. Besides these constraints, the approach takes into consideration the program termination condition for recursive predicates. The paper outlines some theoretical issues and implementation aspects of our system for automatic logic program induction.

A study of reliability-centred maintenance in maritime operations

Abstract This paper has identified specific problems likely to be encountered in endeavour of implementing reliability-centred maintenance (RCM) on ships. These stem out of the cultural differences between the aviation and maritime industries. In the maritime industry, RCM is often considered resource demanding. It is however possible to make the project manageable by starting with a critical system. Considerable savings in time and effort can also be achieved by using a reverse logic where the failure modes are identified by analysing the maintenance tasks. A subjective qualitative approach has been proposed to overcome the limitations of the definitive logic used by the decision trees and the demand for failure data imposed by quantitative methods. A fuel oil purification system has been used as a test case to demonstrate its use. There is appreciation amongst both classification societies and equipment suppliers of the principles of RCM in the maritime industry. This makes the application of the RCM concept feasible. Finally it is the seafarer, who will have to be on the forefront of this endeavour and total productive maintenance can be used to create the right work environment to achieve this. It is concluded that rather than looking at RCM as a methodology and trying to use it as such, it makes more sense to consider it as a philosophy and use its guiding principles to help the seafarer plan his maintenance strategy.

Hybrid Probabilistic Logic Programs as Residuated Logic Programs

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics.

El pensamiento griego en la lógica de Ibn Hazm. Su Kitab al-taqrib

The first book consecrated to logic, written by an andalusian author is Ibn Hazm’s Kitab al-taqrIb li-Eadd al-manðiq (“Introduction to definition of logic”). Where, the author seeks to adapt the logic to the simple language of the jurists. Here it is pointed out how this important treatise can depend on the logical school of Bagdad.