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We present PERPLEX, a programming environment intended for the end-user. In its design, the concepts of logic programming and spreadsheets are combined. Thus, on the one hand, logic programming becomes an interactive, incremental task where the user gets direct visual feedback, on the other hand, functionality and scope of a conventional spreadsheet program are considerably extended. In order to perform calculations and queries, constraints are imposed on the contents of the spreadsheet cells. New predicates can be defined using a programming-by-example technique: Rules are extracted from the user's solutions for example problems. Thus, concrete intermediate results take over the role of abstract logic variables in the programming process. PERPLEX has been successfully implemented on a Symbolics Lisp Machine.

Practitioners of disciplines whose problems are debated by moral philosophers regularly complain that the philosophers are engaged in abstract speculation, divorced from ‘real-life’ consequences and responsibilities, that it is the practitioners (doctor, research scientist, politician) who must take the decisions, and that they cannot (and should not) act in accordance with strict abstract logic.

The logician recognizes the following propositional forms as necessary and sufficient for the expression of any truth

Logic response statistics are developed for a class of randomly interconnected zero memory logic nets which are frequently used in the so-called learning systems. From these statistics, it is shown that it is possible to obtain the probabilities of the transmission characteristics of the randomly interconnected logic networks once the interconnections probabilities are known. The method of identification shown here follows one developed in an earlier paper of Wolf and Wolf and Dietz with minor modifications to account for the logic nature of the networks. Following the previous work, an ergodic probe is used as the stimulus to excite all modes of operation of the zero memory logic networks in order to identify the transmission probabilities. The probe in this case is not white noise, but rather binary noise. An example is shown of a logic system consisting of two inputs and a single output with randomly interconnected elements. This logic system is identified in terms of the probabilities of interconnection and the logic response statistics.

Dr. E. V. HUNTINGTON has recently given two different definitions of abstract groups by sets of respectively three t and four ilndependent postulates; these definitions were perhaps suggested by those given by WEBER and by BURNSIDE. Some years ago Professor J. PIERPONT and I independently hit on a type of definition very desirable from the grouptheoretic stanidpoint. In ? 1 I formulate a definiition of this type by means of five independent postulates; the independence is proved in ? 4. In ? 3 the definition is related to other definitionis. In this connection I am led to a slightly modified definition (p. 489) by means of six independent postulates, which, even from the standpoint of abstract logic, seems to me simpler than either of those of Dr. HUNTINGTON. ? 1. THE DEFINITION.

ive set. The intrinsic character of an event-particle is expressed in terms of certain physical properties of nature at an instant. And these physical properties are expressed in terms of material objects (electrons, etc.). The physical character of an event arises from the fact that it belongs to the field of the whole complex of such objects. From another point of view we can say that these objects are nothing else than our way of expressing the mutual correlation of the physical characters of events.'0' Intersecting moments, abstractive sets, and scientific objects, respectively, endow event-particles with their three fundamental characteristics. We now consider the last of these three factors, scientific objects. It should be stated at once that electrons and molecules are but two types comprising what are called "material objects," a piece of wood in a chair, etc., being also a material object. Scientific objects are material objects exhibiting pronounced definiteness and permanence, these characters being even more present in electrons than in a molecule.'02 A third characteristic of scientific objects is their imperceptibility. . ..no one has seen a single molecule or a single electron, yet the characters of events are only explicable to us by expressing them in terms of these scientific objects.103 In The Principles of Natural Knowledge Whitehead expresses the same view: Scientific objects are not directly perceived, they are inferred by reason of their capacity to express these characters [the characters of events in their capacity of active conditioning events for sense-objects], namely, they express how it is that events are conditions. In other words they express the causal characters of events.'04 This brief statement reminds us that like the extrinsic character and the positional character of an event-particle, the intrinsic character of an event-particle is at least partly conceptual in its origins. This qualitative feature is derived from the ingression of an object "not disclosed in sense-awareness but known by logical inference as necessarily in being,"''05 that is, "not posited by senseawareness ... [but] known to the intellect."'06 The non-natural character of scientific objects depends upon their lying beyond what is given in sense-awareness, and this fact Whitehead confesses in one passage in Th6 Principles of Natural Knowledge. Now electrons-in so far as they are ultimate scientific objects and if they are such objects -do not satisfy the complete condition for recognisability.107 We remember that recognizability is what defines objects as distinct from events, events being "apprehended." Moreover, it is interesting to notice in this connec1olOp. cit., p. 193. 1020p. Cit., pp. 171-172. 1O3Op. cit., p. 171. 104PNK, P. 95. 1O6CN, p. 126. 106Op. cit., p. 125. 107PNK, p. 98. This content downloaded from 157.55.39.148 on Tue, 12 Jul 2016 05:22:13 UTC All use subject to http://about.jstor.org/terms 162 NATHANIEL LAWRENCE tion that Whitehead does not always place such undivided confidence in what logic and thought require as he does in the passage cited above. Indeed we may well be sceptical as to these ultimate entities at points, and doubt whether there are any such entities at all. They have the suspicious character that we are driven to accept them by abstract logic and not by observed fact.'08 The atomic character of nature which is traceable to ingredient objects is, however, achieved by scientific objects, even though they are beyond perception. "A molecule requires a minimum of duration in which to display its character. "09 It is possible therefore that for the existence of certain sorts of objects, e.g. electrons, minimum quanta of time are requisite. Some such postulate is apparently indicated by the modern quantum theory and it is perfectly consistent with the doctrine of objects maintained in these lectures."' The minimum quantity of time which the method of extensive abstraction would not permit us to discern, for that method has as a fundamental postulate the denial of the presence of a "smallest event" in an abstractive set, is thus required by the ultimate objects of science in order that they may be present in nature, either as "situated" in events or as "located" in an abstractive element. As long as entities inferred from events comprising abstractive sets be regarded not merely as "ideal" and "abstract" in character, but also as conceptual, that is, instrumental in bringing precision and simplicity to the analysis of nature, in rendering nature (as the terminus of sense-awareness) intelligible, and not present in nature, there is no conflict. There is ample evidence for such interpretation of Whitehead. But when we try to make of these inferred entities things actually present in nature, in the face of insisting that there is but one nature"' and that nature is what we are aware of in perception,"12 then conflicts arise. Scientific objects then become as genuinely ingredient in nature as, let us say, the sense object "red"; the events they occupy are as actual as the event which is last month's plane crash, and we encounter a host of difficulties and contradictions, for both objects and events have been extended beyond the limits imposed on them by the character of the means by which they were obtained. They are illegitimately transferred from what sense-presentation requires us to think to the realm of sense-presentation itself.

Logic circuits knowledge is the cornerstone of all the courses devoted to digital systems design. Therefore, it is important to ensure a high level of knowledge, understanding as well as the skills of all the students of informatics and computer science study programs. The present study introduces a method to improve the students‟ results by the means of a multi-purpose virtual verification panel called FitBoard. The above mentioned tool is focused specifically on understanding and practicing the complete set of logic gates. However, the tool also provides many additional features. FitBoard is platform independent, easy to use, configurable for various tasks and restrictions and useful in learning as well as in the assessment process. Compared to the other available logic gates simulators, the simplicity and intuitive user interface of FitBoard enables the students to concentrate on the assigned tasks without first studying the usage. The data collected during the course proved a positive response from both the teachers as well as the students.

Logic programming-s application in knowledge based systems require heavy use of images for effective human interfaces;, and it needs powerful methods for describing, generating images. PROLOG as an AI language gives the user the possibility to describe concepts – in this way images - at very high level and can solve problems given declaratively as well. The high need of computer graphics in logic programming languages and the lack of it in present PROLOG implementations motivated us to elaborate a graphic system built into MPROLOG language and to analyze its role in AI applications. A 3-dimensional graphics – called eagle graphics – based on turtle graphics was created. An implementation is briefly described.

Publisher Summary Definability in an abstract logic is compared with definability in a set theory. This leads to set theoretical characterizations of implicit definability, Lowenheim-numbers, and Hanf-numbers of various abstract logics. A new logic, sort logic, is introduced as the ultimate limit of abstract logics definable in set theory. This chapter discusses both old and new results about unbounded abstract logics and illustrates typical problems in any logic—model classes that are implicitly definable, classes of cardinals that are spectra, Lowenheim-number, and Hanf-numbers. In the case of unbounded logics these problems are relevant because such logics fail to be axiomatizable and mostly lack a workable model theory.

This is an expository paper. My aim is to explain in a way accessible to the non-specialist a number of results that amount to characterizations of elementary logic (EL), i.e. first order predicate logic with identity. The characterizations that I have in mind can be described as follows: First I define the very general concept abstract logic (AL). Then I define an inclusion relation ⊆ between ALs. Intuitively L⊆L′ means that everything that can be expressed in L can also be expressed in L′ although perhaps in a different way. For example, in EL it can be said of a binary relation that it is transitive. Thus if EL⊆L, this can also be expressed in L. (I assume, of course, that EL is an AL) L and L′ are equivalent, L≡L’ if L⊆L′ and L′⊆L. The next step consists in choosing a number of properties P 1,…,P n of ALs such that EL has P 1,…, P n . An example of an interesting property of this type is the following which may be called the Lowenheim property, since it means that the original Lowenheim theorem holds for L: If a sentence of L has a model, then it has a countable (finite or denumerable) model. Finally, a characterization of EL is a (true) statement of the form: If L is an AL, EL⊆L, and L has P 1,…, P n , then L≡EL. Since all reasonable ALs contain EL, this may also be expressed by saying that EL is the strongest AL having P 1,…, P n . Of course, one can also speak of characterizations of logics other than EL and there are, in fact, results of this type but they will not be discussed here.

In his paper ‘History of Mathematics: Why and How’ for the 1978 International Congress of Mathematicians in Helsinki, Andre Weil makes the following statement: »Some universities have established chairs for ‘the history and philosophy of mathematics’; it is hard for me to imagine what those two subjects can have in common.» (Weil, 1980, p. 230.)

Logic database queries are often inquired in different ways, which in turn may require different processing strategies. We study the possible strategies of processing recursive queries and the methods of selecting such strategies. Recursive query processing strategies are classified into four classes: non-recursive, total closure, query closure and existence checking, which can be further divided into binary and unary algorithms. A method is developed for selecting appropriate strategies based on IDB compilation results, variable instantiations and inquiries of query predicates, and database statistics. Primitive single- and multi-chain recursions are taken as typical examples in our analysis, however, the principles discussed here are applicable to more complex recursions as well.

Logic programming languages for database applications, such as LDL, and NAIL! [5] generate all solutions for a given query and fail to recognize multiple equivalent, i.e., redundant, solutions. The Prolog solution is to use the cut operator. Ideally, one would like to syntactically identify programs in which redundant solutions may be pruned but one faces undecidability results in this direction. In order to circumvent the recognition problem we provide an explicit construct, called choice, to choose subsets of relations. We show that choice has clean bottom-up semantics and subsumes the Prolog cut and existential queries.

Regardless of any doctrinal views of the matter, it is clear that with respect to a wide spectrum of propositions we are not in a position to say whether they are true or false. (E. g., “The President of the U. S. A. in the year 2010 will have been trained as a physician.”) And this is most graphically the case in those matters with respect to which we ourselves deliberate regarding our line of conduct. (E. g., “Smith will do A” in a context in which Smith is endeavoring to decide whether to do A or B.) In such cases, the temptation may come upon us to hold not simply that one cannot yet say whether the statement at issue is true or false, but to hold that the statement does not yet have any truth-value whatever. Although the points at issue may seem to involve only matters of abstract logic, this appearance is deceptive, for important philosophical doctrines are critically involved. Consider the argument: (1) All propositions have a truth-value, and these truth-values do not change over time. (2) Therefore, propositions about my actions tomorrow were already true (or false) yesterday, and consequently. (3) My deliberations and decisions today can have no influence upon my actions tomorrow.

Logic circuits operating in living cells are generally built by mimicking electronic layouts, and scale-up is accomplished using additional layers of elementary logic gates like NOT and NOR gates. Recombinase-based logic, in which logic is implemented using DNA inversion or excision, allows for highly efficient, compact and single-layer design architectures. However, recombinase logic architectures depart from electronic design principles, and gate design performed empirically is challenging for an increasing number of inputs. Here we used a combinatorial approach to explore the design space of recombinase logic devices. We generated combinations and permutations of recombination sites, genes, and regulatory elements, for a total of ~19 million designs supporting the implementation of all 2- and 3-input logic functions and up to 92% of 4-input logic functions. We estimated the influence of different design constraints on the number of executable functions, and found that the use of DNA inversion and transcriptional terminators were key factors to implement the vast majority of logic functions. We provide a user-friendly interface, called RECOMBINATOR (http://recombinator.lirmm.fr/index.php), that enable users to navigate the design space of recombinase-based logic, find architectures implementing a specific logic function and sort them according to various biological criteria. Finally, we define a set of 16 architectures from which all 256 3-input logic functions can be derived. This work provides a theoretical foundation for the systematic exploration and design of single-layer recombinase logic devices.

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

We present a framework for the combination of Constraint Logic Programming (CLP) and higher-order Hereditary Harrop Formulas (hoHH). Our aim is to improve the expressiveness of traditional Logic Programming with the benefits of both fields: CLP and hoHH. The result is denoted higher-order Hereditary Harrop Formulas with Constraints (hoHH(C)). The syntax of hoHH is introduced using lambda-terms and is enriched with a basic constraint system. Then an intuitionistic sequent calculus is defined for this combined logic, that preserves the property of an abstract logic programming language. In addition, a sound and complete procedure for goal solving is presented as a transformation system that explains the operational semantics.