Functional Logic Programming

Online reviews are a feedback to the product and play a key role in improving the product to cater to
consumers. Online reviews that rely heavily on manual categorization are time consuming and labor
intensive.The recurrent neural network in deep learning can process time series data, while the long and
short term memory network can process long time sequence data well. This has good experimental
verification support in natural language processing, machine translation, speech recognition and language
model.The merits of the extracted data features affect the classification results produced by the classification
model. The LDA topic model adds a priori a posteriori knowledge to classify the data so that the
characteristics of the data can be extracted efficiently.Applied to the classifier can improve accuracy and
efficiency. Two-way long-term and short-term memory networks are variants and extensions of cyclic neural
networks.The deep learning framework Keras uses Tensorflow as the backend to build a convenient two-way
long-term and short-term memory network model, which provides a strong technical support for the
experiment.Using the LDA topic model to extract the keywords needed to train the neural network and
increase the internal relationship between words can improve the learning efficiency of the model. The
experimental results in the same experimental environment are better than the traditional word frequency
features.

The spreadsheet application is among the most widely used computing tools in the modern society. It provides great usability and usefulness, and it easily enables a non-programmer to perform programming-like tasks in a visual tabular " pen and paper " approach. However, due to its mono-directional dataflow, spreadsheets are mostly limited to bookkeeping-like applications. This paper shows how the spreadsheet computing paradigm is extended to break through this limitation for solving constraint satisfaction problems. We present an enhanced spreadsheet system where finite-domain constraint solving is well supported in a visual environment. A spreadsheet-specific constraint language is constructed for general users to specify constraints among data cells in a declarative and scalable way. The new spreadsheet system significantly simplifies the development of many constraint-based applications using a visual tabular interface. Examples are given to illustrate the usability and usefulness of the extended spreadsheet paradigm.

Civil society has emerged as a central force in peacebuilding and is contributing to the reframing of discourse around the concept. Despite the interest in Civil Society Organisations (CSOs) peacebuilding activities, little has been done to suggest a functional perspective to CSOs contribution to peacebuilding. What seems to exist is a largely descriptive account of civil society peacebuilding initiatives based on its forms and actors rather than its functions. It is within this context, that this paper, examines, civil society and peacebuilding. It provides an analytical framework to better understand the functions of civil society and sketches their growing involvement in peacebuilding. The thesis sponsored by this paper is that a functional analysis of CSOs in peacebuilding would enable stakeholders and funders to better analyze existing and potential forms of CSOs engagement in peacebuilding. The paper argues that civil society contributions to peacebuilding can be categorized in a variety of ways, but stakeholders and particularly donors largely employ actor-oriented perspectives which have often denied the concerned public knowledge of the contributions of CSOs to peacebuilding. It proposes to move toward a functional perspective; centered on the roles that CSOs can play in peacebuilding. The paper identifies the functional perspective of CSOs to include: protection, monitoring/early warning; advocacy/public communication; socialization, social cohesion; intermediation/facilitation and service provision. It maintains that these seven functions encompass the core roles of civil society and that taken together offer a suitable framework to better understand the potential contribution of civil society to peacebuilding.

Motivated by the goal of being able to manipulate complex objects symbolically, we propose a method of integrating functional, logic and object-oriented programming paradigms. Our method assumes the existence of an object-expression evaluator (i.e. the underlying Smalltalk interpreter) and relies on transformations and calls to this object-expression evaluator as its means of computation. Programs of the combined paradigm consist of conditional rewrite rules augmented to incorporate object expressions. 1

To date, a number of researchers are seeking for and/or designing novel molecules which function as arithmetic molecular engines. Biomolecules such as deoxyribonucleic acid (DNA) and proteins are examples of promising candidate molecules. In the present article, we showed our view that DNA-based molecules could be used as a novel class of platforms for discrete mathematical operations or tools for natural computation. Here, we report on a novel molecular logic circuit combining exclusive disjunction (XOR) gate and conjunction (AND) gate implemented on a single DNA molecule performing arithmetic operations with simple binary numbers through polymerase chain reactions (PCR); which was inspired by previously developed protein-based computing model allowing simple polynomial algebra over fields through algebraic representation of cyclic inter-conversions in the catalytic modes of a plant enzyme as a cyclic additive group. In addition, we showed that DNA can be used as the platform for image coding and processing leading to DNA-coded animation by using novel PCR-based protocols. Lastly, we discussed the significance of recent attempts in the stream of natural computing and synthetic biological research, by handling DNA and related biomolecules as the media for discrete mathematical operations.

Whereas ordinary types approximate the results, session types approximate communication among computations. As a form of typestate, they describe not only what is communicated now but also what is to be communicated next. Writing session-typed programs in an ordinary programming language such an OCaml requires inordinary cleverness to simulate type-level computations and linear typing – meaning the implementation and the error messages are very hard to understand. One is constantly reminded of template metaprogramming in C++. We present a system exploring a very different approach to session typing: lowering type-level sophistry to ordinary programming, while maintaining the static assurances. Error messages are detailed and customizable, and one can use an ordinary debugger to investigate session-type problems. Our system is a binary-session–typed DSL for service-oriented programming in OCaml, supporting multiple communication channels, internal and external choices, recursion, and...

The paper introduces a method of transition from Transparent Intensional Logic (TIL) into Prolog system and vice versa, in order to utilize Prolog inference machine in the deductive system of TIL. Agents communicate in the TIL-Script language, a computational variant of the expressive TIL system, which serves as a content language of agents’ messaging. However, since a great expressive power is inversely proportional to an easy implementation of a suitable automatic deductive system, we specify a subset of the set of TIL constructions the elements of which can be encoded in Prolog language. Moreover, due to the weaker expressivity of Prolog we have to build up a TIL functional overlay that makes it possible to realize the reverse transition from Prolog into TIL in a near to equivalent way.

The scandal of deduction? Bulletin of Symbolic Logic, 20 (2014) 132–3. 

  Deduction produces no information—in one sense of produce information: propositions provable by deduction alone are tautological, uninformative, devoid of information; likewise, any information contained in a conclusion deduced from given premises was already contained in those premises. In this sense, deduction is informationally unproductive.
  Nevertheless, deduction is clearly instructive—people learn something doing a deduction. Deduction produces knowledge, which is sometimes also called information.
  The above has been found puzzling or even paradoxical. Hintikka wrote—without references or argumentation—that no one had yet explained in what sense deduction produces information. He used the expression the scandal of deduction to describe the situation.
  We survey the literature for explanations of the senses in which deduction produces information.

This paper deals with the study of existence, uniqueness and stability of solutions of fractional integro-differential equations involving Caputo derivative in Banach spaces. Our tools employed are fractional calculus, Hölder inequality and Darbo-Sadovskii fixed point theorem via Hausdorff's measure of non-compactness.

CORCORAN ON QUINE’S PHILOSOPHY OF LOGIC
Corcoran, J. 1972. Quine, Willard. Philosophy of Logic. In Philosophy of Science 39, 97–99.
WILLARD QUINE, Philosophy of logic, Harvard, 1970/1986.

This book is best regarded as a concise essay developing the personal views of a major philosopher of logic and as such it is to be welcomed by scholars in the field. It is not (and does not purport to be) a treatment of a significant portion of those philosophical problems generally thought to be germane to logic. It would be easy to list many popular topics in philosophy of logic which it does not mention. Even its "definition" of logic-"the systematic study of logical truth"-is peculiar to the author and would be regarded as inappropriately restrictive by many logicians
  There are several standard ways of defining truth using sequences. Quine’s discussions in the 1970 first printing of Philosophy of logic and in previous lectures were vitiated by mixing two. Quine’s logical Two-Method Error, which eluded Quine’s colleagues, was corrected in the 1978 sixth printing. But Quine never explicitly acknowledged, described, or even mentioned the error in print although in correspondence he did thank Corcoran for bringing it to his attention.
In regard to style one may note that the book is rich in metaphorical and sometimes even cryptic passages one of the more remarkable of which occurs in the Preface and seems to imply that deductive logic does not warrant distinctive philosophical treatment. Moreover, the author's sesquipedalian performances sometimes subvert perspicuity.

Building on the notational principles of C. S. Peirce’s graphical logic, Pietarinen has tried to develop a propositional logic unfolding in the medium of sound. Apart from its intrinsic interest, this project serves as a concrete test of logic’s range. However, I argue that Pietarinen’s inaugural proposal, while promising, has an important shortcoming, since it cannot portray double-negation without thereby portraying a contradiction.

CORCORAN AND NAMBIAR ON PEANO’S SCHOOL

This article is part of an ongoing project to describe the results actually obtained by Peano and the Italian School, to examine the motivations behind the research, and to assess the influence of these results on later developments in logic and foundations of mathematics. There are rich philosophical and historical results in this article. For example, it establishes by persuasive quotations from Peano's writings that Peano subscribed to what might be called the "double-use conception of logical principles", the view that logical principles not only serve as premises from which inferences are made, but also justify inferences by serving as rules according to which inferences are made. The double-use conception, so alien to contemporary thinking and so far (except for this article) totally ignored by contemporary philosophers and historians, seems to have been transmitted by Peano to Russell, Whitehead, Lewis, Baylis, and other logicians. For more on double-use, see the following.
https://www.academia.edu/26417165/CORCORAN_ON_C_I_LEWIS

LOGICAL METHODOLOGY CHART
Charting a method for trying to determine the validity or invalidity of a given argument not known to be valid and not known to be invalid

METHOD OF DEDUCTION: An argument is valid iff its conclusion follows from its premise-set. Not every valid argument is known to be valid. To determine of a given valid argument not now known by you to be valid, you need a method that produces knowledge of validity. One method in use before Aristotle is to deduce the conclusion from the premises-set.
METHOD OF COUNTERARGUMENTATION: An argument is invalid iff its conclusion does not follow from its premise-set. Not every invalid argument is known to be invalid. To determine of a given invalid argument not now known by you to be valid, you need a method that produces knowledge of invalidity. One method, perhaps not in use before Aristotle, is to produce a known counterargument: an argument known to be in the same form, known to have a falsehood as its conclusion, and known to have all truths in its premises-set.

This paper will investigate the general class theory of polycalculii, and theory originally developed and introduced on the Quora platform as a kind of philosophy of logic and mathematics. The ostensible goal at minima will be to demonstrate the exclusion of an array of class types which edicate the theorem of the polycalculus. The polycalculus is a general method for deriving equivalent calculus’s other than the traditional intelligent calculus. The domain of this discussion is not only mathematics, but also logic, philosophy, and philosophy of science, as well as philosophy of the foundations of mathematics.

Biocomputing is a recently growing and highly interdisciplinary field of research that investigates models and computational techniques inspired by biology and related sciences. Here, cyclic behavior (redox cycling) of purified horseradish peroxidase protein among native enzyme and its two electron-oxidized and single electron-oxidized intermediates known as Compounds I and II was algebraically expressed as a cyclic additive group Z 3 = {C 0 , C 2 , C 1 } = {C 0 , 1C 2 , 2C 2 } = {0, 2, 1}, and a cyclic multiplicative group Z * 3 = {C 1 , C 2 } = {C 1 , C 1 2 } = {1, 2}, with C 2 as the common generator. Above algebraically expressed features of the enzyme's redox cycle was applied to help determining the coefficients in polynomials formed after additive and/or multiplicative operations between polynomial rings f (x) and g(x) over a coefficient field derived from Z 3. Similarly, use of a pair of small DNA molecules was proposed for determining the coefficients for additively and multiplicatively obtained polynomials over F , (Z 2 ; +, ×); where Z 2 = {C 0 , C 1 } = {0, 1}. Discussion includes the required designs of two distinct DNA molecules for performing binary logical conjunction (AND) and exclusive disjunc-tion (XOR), upon polymerase-chain reactions.

Corcoran, John. 1999. Logical form, The Cambridge Dictionary of Philosophy, edited by Robert Audi, Cambridge, Cambridge University Press, second edition.

LOGICAL FORM, the form obtained from a proposition, a set of propositions or an argument by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, or an argument is determined by the grammatical form of the sentence, the set of sentences, or the argument-text expressing it. Modern formal languages used in formal axiomatizations of mathematical sciences are often taken as examples of logically perfect languages. Pioneering work on logically perfect languages was done by George Boole (1815-64), Gottlob Frege (1848-1925), Giuseppe Peano (1858-1952), Bertrand Russell (1872-1970) and Alonzo Church (1903-1995).

International journal of Programming Languages and applications is dedicated to the distribution of research results in the areas of Programming Languages and applications.

Authors are solicited to contribute to the journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of Programming Languages.

By logic I mean the subject Aristotle started in Prior Analytics. Logic studies demonstration and everything necessary for demonstration, and also many things that come to mind in the course of such studies—including axiomatic method as described in my short “Axiomatic method”. By young I mean less than about 40 years old. By logicians I mean people who have dedicated their lives to advancing and criticizing logic: to discovering and establishing new additions and also to clarifying and correcting what has or had been accepted. More specifically, my advice is for people who have already embarked on their careers: from fresh PhDs, instructors, and assistant professors to young professors looking forward to reaping the fruits of their long years of study and research. My advice is for people who have mastered logic and who want to improve their mastery.

Tuberculosis is an airborne disease that affects many organs in the body especially lungs. This disease is caused by a bacteria known as Mycobacterium Tuberculosis. When the bacteria becomes active it affects the body. If the disease is not treated properly a loss of life may occur. A robotic detection of tuberculosis is presented in this paper with the help of patient chest x ray(CXR).The input image is then filtered by Gaussian filter to remove noise and then the lung region gets segmented by using graph cut segmentation. The segmented lung region is partitioned into four lobes. The infected region is then segmented for that region the feature values are calculated. With these values it is classified as normal or abnormal by using Ada boost classifier.

A person who states that four is square predicates, or affirms, the property being square of the number four. Here the action verb ‘to predicate’ is used to express a three-place action: a person predicates a property of an entity.
  In the sentence ‘four is square’, the word ‘four’ is the [grammatical] subject and ‘is square’ is the predicate. Here the word ‘predicate’ is part of an expression for a two-place grammatical relation: a phrase is the [grammatical] predicate of a sentence. In a third sense, any phrase that occurs as the predicate of a sentence is a predicate, using the word as a non-relational common noun.
  A person who states that four is a number that is a square that is even predicates the property being a number that is a square that is even of the number four. The 10-word phrase

is a number that is a square that is even

is the grammatical predicate of the 11-word sentence ‘four is a number that is a square that is even’ although that sentence contains occurrences of five other predicates: ‘is a number that is a square’, ‘is a number’, ‘is a square that is even’, ‘is a square’ and ‘is even’. A person who uses the 11-word sentence to state that four is a number that is a square that is even makes one predication, but uses six predicates.
  This lecture is an introduction to a neglected topic: the uses of the words ‘predicate’ and ‘predication’ in logic. Authors discussed include Aristotle, Boole, DeMorgan, Peirce, Frege, Russell, Tarski, and Church. It builds on lectures abstracted in this BULLETIN vol. 11(2005) p. 117 and vol. 12(2006) pp. 353-4.

CORCORAN ON PUTNAM’S PHILOSOPHY OF LOGIC
A 1973 review of Putnam's 1972 Philosophy of Logic. In Philosophy of Science 40, 131–33.

Philosophers of science, not simply logicians, will find much of interest in this book (despite its title). Within its extremely short length it provides a substantive overview of the role of abstract entities in science and it employs as many examples and arguments from physics as from mathematics and logic. This is one of those rare books which is both elementary without being trivial and sophisticated without either being overly intricate or presupposing a vast background of knowledge. Students of logic and/or philosophy of science will gain as much from this book as their professors—but the students may not be able to appreciate the depth of the thought that has gone into it.
From one point of view the book can be seen as an essay-length argument designed to show that modern versions of nominalism are intellectually dishonest and antiscientific and that a rational and undogmatic acceptance of modern science presupposes a realistic (platonistic) stance in regard to abstract entities. But it is more as well. The first half includes a critique of the Leblanc-Quine substitution conception of logical truth and an argument against limiting the scope of logic to the first order. The second half which can be read for the most part without the first half) concerns the role of abstract entities in physics and higher mathematics and it presents arguments against various attempts to "fictionalize" them and/or to "eliminate" them from the ontology of modern science.

Reviewer: John Corcoran.
Acknowledgements: David Braun, William Demopoulos, Thomas Drucker, Warren Goldfarb, Idris Samawi Hamid, Allen Hazen, Harold Theodore Hodes, David Marans, Hassan Masoud, Christopher Menzel, Joaquin Miller, Frango Nabrasa, Sriram Nambiar, Stephen Read, José Miguel Sagüillo, Michael Scanlan, Kevin Tracy, Jeffrey Welaish, George Williams, and others.
Special thanks to Warren Goldfarb, Idris Samawi Hamid, Allen Hazen, Harold Theodore Hodes, Christopher Menzel, Joaquin Miller, and Kevin Tracy for instructing me in the nuances of this important but Byzantine field.

CONTENTS
REVIEW TEXT 12
REFERENCES
QUOTES

REVIEW TEXT
DRAFT 12 012616 730AM
The article under review titled “Why ramify?”—hereafter WR—revisits investigations in logic and foundations of mathematics spanning three centuries. WR is a massive effort: 36 pages long, 57 references, 77 footnotes. WR is replete with delicate philosophical arguments buttressed with interesting quotations, intricate mathematics, and contemporary symbolic logic; its stated purpose “is not to defend or criticize any philosophical view but rather to better understand Russell’s philosophy and his century-old project in the foundations of logic and mathematics” [REFERENCE WR, p. 380].
WR’s subject is the theory of types, hereafter TT, initially conceived by Bertrand Russell before 1903 and intended to deal with paradoxes prominent in the 1800s [REFERENCE 1908]. After some reworking, TT formed the basis of the monumental Principia Mathematica by A. N. Whitehead and B. Russell [REFERENCE PM]. TT is still of intense interest to historians of mathematics, of logic, and of philosophy. Understanding TT is a prerequisite for mastery of modern logic.
However, today TT is no longer as important as it once was as an active research topic for modern logicians, who regard it as higher-order logic, in fact, as logic of infinite order. On the contrary, modern investigations focus largely on first-order logics—the weakest sub-logics of TT adequate to serve as underlying logics of sciences. Today opposition to TT is so intense that it is felt necessary to defend the mere teaching of second-order logic [REFERENCE C]. In the late 1970s Alfred Tarski said that results achieved using just second-order logic are “meaningless” [REFERENCE CS]. However, one cannot predict a future without second-order logics or even higher-order logics. Indeed, some logicians discern indications that the pendulum might be starting to reverse.

Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth)
Also see https://www.academia.edu/s/a6bf02aaab
This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point of view.  In normal English these two sentences are idiomatically taken to express the true proposition that ‘the number 3 is the number 2+1’.
Another idiomatic convention that interferes with clarity about equality and identity occurs in discussion of numbers: it is usual to write ‘3 equals 2+1’ when “3 is 2+1” is meant. When ‘3 equals 2+1’ is written there is a suggestion that 3 is not exactly the same number as 2+1 but that they merely have the same value. This becomes clear when we say that two of the sides of a triangle are equal if the two angles they subtend are equal or have the same measure.

Acknowledgements: Robert Barnes, Mark Brown, Jack Foran, Ivor Grattan-Guinness, Forest Hansen, David Hitchcock, Spaulding Hoffman, Calvin Jongsma, Justin Legault, Joaquin Miller, Tania Miller, and Wyman Park.

► JOHN CORCORAN AND ANTHONY RAMNAUTH, Equality and identity.
Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA
E-mail: corcoran@buffalo.edu
  The two halves of one line are equal but not identical [one and the same]. Otherwise the line would have only one half! Every line equals infinitely many other lines, but no line is [identical to] any other line—taking ‘identical’ strictly here and below.
  Knowing that two lines equaling a third are equal is useful; the condition “two lines equaling a third” often holds. In fact any two sides of an equilateral triangle is equal to the remaining side! But could knowing that two lines being [identical to] a third are identical be useful? The antecedent condition “two things identical to a third” never holds, nor does the consequent condition “two things being identical”. If two things were identical to a third, they would be the third and thus not be two things but only one.
  The plural predicate ‘are equal’ as in ‘All diameters of a given circle are equal’ is useful and natural. ‘Are identical’ as in ‘All centers of a given circle are identical’ is awkward or worse; it suggests that a circle has multiple centers.
  Substituting equals for equals [replacing one of two equals by the other] makes sense. Substituting identicals for identicals is empty—a thing is identical only to itself; substituting one thing for itself leaves that thing alone, does nothing.
  There are as many types of equality as magnitudes: angles, lines, planes, solids, times, etc. Each admits unit magnitudes. And each such equality analyzes as identity of magnitude: two lines are equal [in length] if the one’s length is identical to the other’s.
Tarski [1] hardly mentioned equality-identity distinctions (pp. 54-63). His discussion begins:

Among the logical concepts […], the concept of IDENTITY or EQUALITY […] has the greatest importance.

Not until page 62 is there an equality-identity distinction. His only “notion of equality”, if such it is, is geometrical congruence—having the same size and shape—an equivalence relation not admitting any unit. Does anyone but Tarski ever say ‘this triangle is equal to that’ to mean that the first is congruent to that? What would motivate him to say such a thing?
  This lecture treats the history and philosophy of equality-identity distinctions.
[1] ALFRED TARSKI, Introduction to Logic, Dover, New York, 1995.

High speed Full-Adder (FA) module is a critical element in designing high performance arithmetic circuits. In this paper, we propose a new high speed multiple-valued logic FA module. The proposed FA is constructed by 14 transistors and 3 capacitors, using carbon nano-tube field effect transistor (CNFET) technology. Furthermore, our proposed technique has been examined in different voltages (i.e., 0.65v and 0.9v). The observed results reveal power consumption and power delay product (PDP) improvements compared to existing FA counterparts

The miniKanren relational programming language, though designed and used as a language with which to teach re-lational programming, can be immensely frustrating when it comes to debugging programs, especially when the programmer is a novice. In order to address the varying levels of programmer sophistication, we introduce a suite of different language levels. We introduce the first of these languages , and provide experimental results that demonstrate its effectiveness in helping beginning programmers discover and prevent mistakes. The source to these languages is found at https://github.com/dabrady/LittleLogicLangs.