Deductive Procedure Research Articles

On the Completeness and Decidability of the Horn‐Like Fragment of the First‐Order Linear Temporal Logic

We prove the completeness and decidability of the Horn‐like sequents, specifically, the so‐called D2‐sequents (of the first‐order linear temporal logic) considered in the author's paper [Lith. Math. J., 41(3), 266–281 (2001)]. In this paper, with the help of the infinitary calculus GLω, grounded by the author in his earlier papers, for D2‐sequents we construct a D2Sat calculus of the so‐called saturated type consisting of decidable deductive procedures replacing the omega‐rule for the “always” operator. In the present paper, in order to prove the completeness and decidability of the calculus D2Sat, we construct the so‐called invariant decidable calculus D2IN. We prove the equivalence of the calculi D2IN, D2Sat, and G Lω ** for the so‐called saturated D2‐sequents. From this equivalence, by reducing an arbitrary D2‐sequent to a saturated D2‐sequent, and also from the ω‐completeness of the G Lω ** calculus and decidability of the invariant calculus D2IN, we deduce the completeness and decidability of the calculus D2Sat in the class of D2‐sequents.

Effective Replaceability of the Omega—Rule for Restricted Sequents of the First–Order Linear Temporal Logic

We consider an effective replaceability of the omega–rule for the “always” operator in a restricted first–order linear temporal logic. This work is a continuation of two previous papers of the author where an infinitary (with the omega–rule) calculus without loop rules was constructed and founded. In the present paper, we use this calculus to construct the so–called saturated calculus consisting of four decidable deductive procedures replacing the omega–rule for the “always” operator.

Recognising deductive processes in qualitative research

States that there are two general approaches to reasoning which may result in the acquisition of new knowledge: inductive reasoning commences with observation of specific instances, and seeks to establish generalisations; deductive reasoning commences with generalisations, and seeks to see if these generalisations apply to specific instances. Most often, qualitative research follows an inductive process. In most instances, however, theory developed from qualitative investigation is untested theory. Both quantitative and qualitative researchers demonstrate deductive and inductive processes in their research, but fail to recognise these processes. The research paradigm followed in this article is a post‐positivist (“realist”) one. This is not incompatible with the use of qualitative research methods. Argues that the adoption of formal deductive procedures can represent an important step for assuring conviction in qualitative research findings. Discusses how, and under what circumstances, qualitative researchers might adopt formal deductive procedures in their research. One approach, theory testing by “pattern matching”, is illustrated with a sample application.

A survey of temporal extensions of description logics

This paper surveys the temporal extensions of description logics appearearing in the literature. The analysis considers a large spectrum of approaches appearearing in the temporal description logics area: from the loosely coupled approaches – which comprise, for example, the enhancement of simple description logics with a constraint based mechanism – to the most principled ones – which consider a combined semantics for the abstract and the temporal domains. It will be shown how these latter approaches have a strict connection with temporal logics. Advantages of using temporal description logics are their high expressivity combined with desirable computational properties – such as decidability, soundness and completeness of deduction procedures. In this survey the computational properties of various families of temporal description logics will be pointed out.

An In-Depth Analysis of the Uses of Imagery by High-Level Slalom Canoeists and Artistic Gymnasts

This study employed a qualitative methodology to examine the ways in which imagery is used by high-level slalom canoeists (n = 3) and artistic gymnasts (n = 3). Participants were interviewed about their imagery use and experiences in different environments. Athletes’ responses were analyzed using inductive and deductive procedures. A total of 43 raw data themes formed 10 first order and 3 second order dimensions, characterizing the athletes’ uses of imagery. Participants reported using imagery in a variety of different environments for cognitive and motivational purposes. Data showed several differences between the canoeists’ and gymnasts’ uses of imagery, reflecting the differing task demands of each sport. The experience of imagery was unique to each individual, and athletes were able to emphasize certain aspects or manipulate the content of their images for specific cognitive or motivational functions.

Development of Proper Models of Hybrid Systems

A method to improve the ability of design engineers to generate proper dynamic models of systems from sets of component models is developed. This two stage method, called Eigenvalue MODA, is a new model deduction procedure for developing proper models of hybrid systems. The first stage in Eigenvalue MODA consists of using a previously published Model Order Deduction Algorithm (MODA) to systematically increment the complexity of each component model in the system. The first stage continues until a set of Critical System Eigenvalues (CSE) has been defined. During the second stage, the complexity component models is incremented based on the convergence of the CSE. The second stage continues until each CSE has converged to within a user specified tolerance. Component models may be represented by first-order (state space) or second-order equations and may be modal expansion or finite segment models. An example shows that the deduction of the proper system model depends on the interactions between the component model representations and the model deduction method. Eigenvalue MODA is a model deduction method that facilitates the generation of models of sufficient accuracy with physically meaningful parameters and states. This makes the models useful for system design and, as such, Eigenvalue MODA would be a useful tool in an automated modeling environment for design engineers.

{\cal A}{\cal L} -log: Integrating Datalog and Description Logics

We present an integrated system for knowledge representation, called{\cal A}{\cal L} -log, based on description logics and the deductive database language Datalog. {\cal A}{\cal L}-log embodies two subsystems, called structural and relational. The former allows for the definition of structural knowledge about classes of interest (concepts) and membership relation between objects and classes. The latter allows for the definition of relational knowledge about objects described in the structural component. The interaction between the two components is obtained by allowing constraints within Datalog clauses, thus requiring the variables in the clauses to range over the set of instances of a specified concept. We propose a method for query answering in {\cal A}{\cal L}-log based on constrained resolution, where the usual deduction procedure defined for Datalog is integrated with a method for reasoning on the structural knowledge.

Humans’ Choice between Different Reinforcer Amounts and Delays: Effects of Choice Procedures and Monetary Deduction

Human subjects were exposed to concurrent-chains schedules in which reinforcer amounts or delays were varied in the terminal links and consummatory responses were required to receive points later exchangeable for money. Two independent variable-interval 30-s schedules or a single variable-interval 15-s schedule were in effect during the initial links and delay periods were defined by fixed-time schedules used in the terminal links. In addition to varying reinforcer amount and delay, two different choice procedures were studied for two different groups and a monetary deduction procedure was studied, within subjects, under independent scheduling procedure. The human subjects preferred the larger of two different reinforcer amounts and the shorter of two different reinforcer delays. The degree of preference was higher in the independent scheduling procedure than in the nonindependent scheduling procedure and there was no substantial difference in preference between the absence and presence of the monetary deduction procedure.

Labelled resolution for classical and non-classical logics

Resolution is an effective deduction procedure for classical logic. There is no similar "resolution" system for non-classical logics (though there are various automated deduction systems). The paper presents resolution systems for intuistionistic predicate logic as well as for modal and temporal logics within the framework of labelled deductive systems. Whereas in classical predicate logic resolution is applied to literals, in our system resolution is applied to L(abelled) R(epresentation) S(tructures). Proofs are discovered by a refutation procedure defined on LRSs, that imposes a hierarchy on clause sets of such structures together with an inheritance discipline. This is a form of Theory Resolution. For intuitionistic logic these structures are called I(ntuitionistic) R(epresentation) S(tructures). Their hierarchical structure allows the restriction of unification of individual variables and/or constants without using Skolem functions. This structures must therefore be preserved when we consider other (non-modal) logics. Variations between different logics are captured by fine tuning of the inheritance properties of the hierarchy. For modal and temporal logics IRS's are extended to structures that represent worlds and/or times. This enables us to consider all kinds of combined logics.

Tabled evaluation with delaying for general logic programs

SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stack-based memory management, SLDNF is often not appropriate for query evaluation for three reasons: (a) it may not terminate due to infinite positive recursion; (b) it may be terminate due to infinite recursion through negation; and (c) it may repeatedly evaluate the same literal in a rule body, leading to unacceptable performance. We address all three problems for goal-oriented query evaluation of general logic programs by presenting tabled evaluation with delaying, called SLG resolution. It has three distinctive features: (i) SLG resolution is a partial deduction procedure, consisting of seven fundamental transformations. A query is transformed step by step into a set of answers. The use of transformations separates logical issues of query evaluation from procedural ones. SLG allows an arbitrary computation rule for selecting a literal from a rule body and an arbitrary control strategy for selecting transformations to apply. (ii) SLG resolution is sound and search space complete with respect to the well-founded partial model for all non-floundering queries, and preserves all three-valued stable models. To evaluate a query under differenc three-valued stable models, SLG resolution can be enhanced by further processing of the answers of subgoals relevant to a query. (iii) SLG resolution avoids both positive and negative loops and always terminates for programs with the bounded-term-size property. It has a polynomial time data complexity for well-founded negation of function-free programs. Through a delaying mechanism for handling ground negative literals involved in loops, SLG resolution avoids the repetition of any of its derivation steps. Restricted forms of SLG resolution are identified for definite, locally stratified, and modularly stratified programs, shedding light on the role each transformation plays.

A typed resolution principle for deduction with conditional typing theory

The formal reasoning involved in solving a real world problem usually consists of two parts: type reasoning associated with the type structure of the problem domain, and general reasoning associated with the kernel formulation. This paper introduces a typed resolution principle for a typed predicate calculus. This principle permits a separation of type reasoning from general reasoning even when the background typing theory shares the same language constructs with the kernel formulation. Such a typing theory is required for an accurate formulation of the type structure of a computer program which contains partial functions and predicate subtypes, and also is useful for efficiently proving certain theorems from mathematics and logic by typed (sorted) formulation and deduction. The paper presents a typed deduction procedure which employs type reasoning as a form of constraints to general reasoning for speeding up the proof discovery. The paper also discusses further refinements of the procedure by incorporating existing refinements of untyped resolution.

Impact de l'article de Davis : la Seine, la Meuse et la Moselle (1895) sur l'étude des paléoréseaux hydrographiques

The impact of Davis's article : « the Seine, the Meuse and the Moselle » (1895) on the study of palaeodrainage Systems. — Davis's paper, « the Seine, the Meuse and the Moselle » is well known for his explanation of the capture of the River Moselle. However, this is only one of many captures that were explained by Davis, and the real significance of his article is that it presented a new explanation of drainage évolution in sedimentary basins. Davis's thesis was not so much a new discovery as a contribution, amongst others. towards the explanation of river capture. An hypothesis to explain the diversion of the Moselle by river capture was first suggested by Buvignier (1840), on the basis of geological evidence. Topographical study of the palaeovalley was undertaken only much later (Godron, 1876). Davis's contribution was the ultimate geomorphological study of river capture. Data from several boreholes finally allowed Nickles (1911) to prove conclusively that the Moselle once flowed through the Val de l'Ane to join the Meuse. The considerable attention given to his views on river capture should not lead to the misapprehension that the main purpose of Davis's article was to demonstrate the occurrence of stream piracy. On the contrary, Davis merely used examples of river capture in a présentation to European scientists of his genetic classification of rivers. Thcre fias been much interest in this classification, although it was not immediately accepted. A. Penck (1899) was the first to endorse it, but French geographers, such as E. de Martonne and P. and J. Vidal de la Blache have argued against its use, as they were sceptical of the deductive procedures advocated by Davis

Anytime deduction for probabilistic logic

This paper proposes and investigates an approach to deduction in probabilistic logic, using as its medium a language that generalizes the propositional version of Nilsson's probabilistic logic by incorporating conditional probabilities. Unlike many other approaches to deduction in probabilistic logic, this approach is based on inference rules and therefore can produce proofs to explain how conclusions are drawn. We show how these rules can be incorporated into an anytime deduction procedure that proceeds by computing increasingly narrow probability intervals that contain the tightest entailed probability interval. Since the procedure can be stopped at any time to yield partial information concerning the probability range of any entailed sentence, one can make a tradeoff between precision and computation time. The deduction method presented here contrasts with other methods whose ability to perform logical reasoning is either limited or requires finding all truth assignments consistent with the given sentences.

Application of the homogenization method to a suspension of fibres

The homogenization method is applied to the determination of a continuum model for an assembly of cylindrical parallel fibres suspended in the longitudinal flow of a viscous incompressible fluid. Whatever the solids concentration is, the homogenization gives the variations of the velocity and the pressure at the level of the microstructure and furnishes a rigorous deductive procedure for obtaining the governing equations of the homogenized bulk medium. The effective constitutive relation is that of a Newtonian incompressible anisotropic fluid. The viscosity is expressed by a second order tensor completely determined by the microstructure. Lower bounds of the viscosity coefficients are found when the microstructure exhibits symmetries. Numerical results are obtained for two cases of macroscopic isotropy. They emphasize the good approximation arising from the lower bounds and the importance of the microstructure geometry for nondilute suspensions. As a matter of fact the solids concentration is not able to describe correctly the influence of the microstructure on the bulk behaviour of concentrated suspensions.

Sound and complete partial deduction with unfolding based on well-founded measures

We present a procedure for partial deduction of logic programs, based on an automatic unfolding algorithm which guarantees the construction of sensibly and strongly expanded, finite SLD-trees. We prove that the partial deduction procedure terminates for all definite logic programs and queries. We show that the resulting program satisfies important soundness and completeness criteria with respect to the original program, while retaining the essentially desired amount of specialisation.

Upside-down meta-interpretation of the model elimination theorem-proving procedure for deduction and abduction

Typical bottom-up, forward-chaining reasoning systems such as hyperresolution lack goaldirectedness, while typical top-down, backward-chaining reasoning systems like Prolog or model elimination repeatedly solve the same goals. Reasoning systems that are goal-directed and avoid repeatedly solving the same goals can be constructed by formulating the top-down methods meta-theoretically for execution by a bottom-up reasoning system (hence, we use the term upside-down meta-interpretation). This formulation also facilitates the use of flexible search strategies, such as merit-ordered search, that are common to bottom-up reasoning systems. The model elimination theorem-proving procedure, its extension by an assumption rule for abduction, and its restriction to Horn clauses are adapted here for such upside-down meta-interpretation. This work can be regarded as an extension of the magic-sets or Alexander method for query evaluation in deductive databases to both non-Horn clauses and abductive reasoning.

Approximate reasoning: Past, present, future

This paper presents a personal view of the state of the art in the representation and manipulation of imprecise and uncertain information by automated processing systems. To contrast their objectives and characteristics with the sound deductive procedures of classical logic, methodologies developed for that purpose are usually described as relying on approximate reasoning. Using a unified descriptive framework, we will argue that, far from being mere approximations of logically correct procedures, approximate reasoning methods are also sound techniques that describe the properties of a set of conceivable states of a real-world system. This framework, which is based on the logical notion of possible worlds, permits the description of the various approximate reasoning methods and techniques and simplifies their comparison. More importantly, our descriptive model facilitates the understanding of the fundamental conceptual characteristics of the major methodologies. We examine first the development of approximate reasoning methods from early advances to the present state of the art, commenting also on the technical motivation for the introduction of certain controversial approaches. Our unifying semantic model is then introduced to explain the formal concepts and structures of the major approximate reasoning methodologies: classical probability calculus, the Dempster-Shafer calculus of evidence, and fuzzy (possibilistic) logic. In particular, we discuss the basic conceptual differences between probabilistic and possibilistic approaches. Finally, we take a critical look at the controversy about the need and utility for diverse methodologies, and assess requirements for future research and development.

Macroscopic and microscopic acid dissociation constants of diprotic acids—A potentiometric and spectrophotometric study

A state-of-the-art survey of the determination of acid dissociation microconstants of diprotic acids is presented. It is shown that potentiometric and spectrophotometric titration data can yield macroscopic constants but are not sufficient to completely resolve the microconstant system unless some sort of assumption is made, which may not always be warranted. Such an estimative deduction procedure is applied to 2,6-di(methylthiomethyl)-3-hydroxypyridine chloride.

Generating and Evaluating International Entrepreneurial Ideas

Much has been written about the role and usefulness of entrepreneurial education in America's dynamic environment beset by a chronic shortage of good entry and career jobs. This paper focuses on two aspects of entrepreneurial education that are decisive to the success of a new venture, yet are hard to teach: (1) how to find profitable, realistic ideas for a new business and (2) how to evaluate them. The author applied the experiential learning approach to these two critical phases of entrepreneurial education in his international marketing classes. He describes five steps that must be taken to introduce this method in the classroom: an Idea Generating Matrix based on deductive procedures and empirical reasoning; a Multifactor Screen to select, postpone, or discard entrepreneurial ideas; a Multilevel Idea Model by applying the case of an ethnic fast food franchise; a Modus Operandi/ Modus Acquirendi Matrix to decide on the operational and acquisition strategy; and a final step, in which reflective and res...

Matching and maximizing in a self-control paradigm using human subjects

Five experiments examined adult human females' sensitivity to variation in amount and delay of reinforcement, as well as their impulsiveness (preference for smaller, less delayed reinforcers over larger, more delayed reinforcers), self-control (the opposite of impulsiveness), and indifference (equal preference for larger, more delayed reinforcers and for smaller, less delayed reinforcers). Each experiment used four to five subjects, concurrent variable-interval schedules, reinforcers that consisted of opportunities to earn points exchangeable for money, and varied relative reinforcer amount and delay separately and/or together. Four experiments used a deduction procedure: a random number of points was repeatedly removed from the display counter at regular intervals, independently of the subjects' behavior. Three experiments used independent concurrent schedules; the other two used nonindependent concurrent schedules. One experiment allowed the subjects to play a radio during laboratory sessions. In all experiments the subjects' behavior was better predicted by a molar maximization model than by the generalized matching law. However, the indifference that occurred when the ratio was used did not closely approximate molar maximization. The deduction procedure appeared to have no effect on the subjects' choices. Use of the nonindependent concurrent schedules seemed to result in the subjects showing indifference and low sensitivity to changes in relative reinforcer amount and delay. Use of the radio also seemed to result in indifference. Unlike the behavior of pigeons, the behavior of adult human subjects within a self-control paradigm appears to be well described by molar maximization, but it may be possible to disrupt such behavior by environmental stimuli.