Deviant Logic, Fuzzy Logic: Beyond the Formalism.

This handbook provides a systematic survey of the central areas of philosophical logic. It is divided into four volumes, each devoted to a major sub-field within the disciplines. The articles should be of value to general philosophers, linguists, logicians, mathematicians and computer scientists. Volume 1, Elements of Classical Logic, deals with the background to what has come to be considered the standard formulation of predicate logic - both as far as its semantics and proof theory are concerned. The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory. In addition, this volume contains a discussion of higher-order extensions of first-order logic and a compendium of the algorithmic and decision-theoretic prerequisites in the study of logical systems. Volume 2, Extensions of Classical Logic, surveys the most significant extensions of predicate logic and their applications to various philosophical fields of inquiry. The 12 chapters in this volume together provide a succinct introduction to a variety of intensional frameworks, a discussion of the most well-known logical systems, as well as an overview of major applications and of the open problems in the respective fields. Volume 3, Alternatives to Classical Logic, consists of a series of surveys of some of the alternatives to the basic assumptions of classical logic. These include many-valued logic, partial logic, free logic, relevance and entailment logics, dialogue logic, quantum logic and intuitionism. Volume 4, Topics in the Philosophy of Language, presents a panorama of the applications of logical tools and methods in the formal analysis of natural language. Since a number of developments in philosophical logic were originally stimulated by concern arising in the semantic analysis of natural language discourse, the chapters in this volume provide some criteria of evaluation of the applications of work in philosophical logic. In revealing both the adequacies and inadequacies of logical investigations in the semantic structures of natural discourse, these chapters also point the way to future developments in philosophical logic in general and thus close again the circle of inquiry relating logic and language.

The past few decades have seen a resurgence of reasoning techniques in artificial intelligence involving both classical and non-classical logics. In his paper, ``Multi-valued Logics: A Uniform Approach to Reasoning in Artificial Intelligence'', Ginsberg has shown that through the use of bilattices, several reasoning techniques can be unified under a single framework. A bilattice is a structure that can be viewed as a class of truth values that can accommodate incomplete and inconsistent information and in certain cases default information. In bilattice theory, knowledge is ordered along two dimensions: truth/falsity and certainty/uncertainty. By defining the corresponding bilattices as truth spaces, Ginsberg has shown that the same theorem prover can be used to simulate reasoning in first order logic, default logic, prioritized default logic and assumption truth maintenance system. Although this is a significant contribution, Ginsberg's paper was lengthy and involved. This paper summarizes some of the essential concepts and foundations of bilattice theory. Furthermore, it discusses the connections of bilattice theory and several other existing multi-valued logics such as the various three-valued logics and Belnap's four-valued logic. It is noted that the set of four truth values in Belnap's logic form a lattice structure that is isomorphic to the simplest bilattice. Subsequently, Fitting proposed a conflation operation that can be used to select sub-sets of truth values from this and other bilattices. This method of selecting sub-sets of truth values provides a means for identifying sub-logic in a bilattice.

It is well known that an important task of the artificial intelligence is to make a computer simulate a human being in dealing with certainty and uncertainty in information. Logic gives a technique for laying the foundations of this task. Information processing dealing with certain information is based on the classical logic. Nonclassical logic including many-valued logic and fuzzy logic takes the advantage of the classical logic to handle information with various facets of uncertainty, such as fuzziness and randomness. Therefore, nonclassical logic has become a formal and useful tool for computer science to deal with fuzzy information and uncertain information. For investigation of several properties, such logics have been represented as algebras, that is, sets with one, two, or more algebraic operations satisfying some conditions inspired by these logics. This inspiration is illustrated by the similarities between the names. We have BCK-algebras and a BCK positive logic, BCI-algebras and a BCI positive logic, and BL-algebras and a basic logic. In many cases, the connection between such algebras and their corresponding logics is much stronger. In this case, one can give a translation procedure which translates all well-formed formulas and all theorems of a given logic L into terms and theorems of the corresponding algebras. In some cases, one can give also an inverse translation. In this case, we say that the given logic and class of such algebras are isomorphic. Nevertheless, the study of algebras motivated by logics is interesting and very useful also in the case when these structures are not isomorphic. An important class of algebras inspired by logic is BL-algebras introduced by Hajek in order to provide an algebraic proof of the completeness theorem of Basic Logic. A classical example of a BL-algebra is the interval [0,1] endowed with the structure induced by a continuous t-norm. Other important examples of BL-algebras are MV-algebras introduced earlier as a model of some infinitely valued Łukasiewicz logic. All these algebras are also strongly connected with residuated lattices. Hence, the filter theory plays an important role in the study of these algebras. From logic point of view, various filters correspond to various sets of provable formulae in the respective logic. Below we present several papers on filters in various algebras. In one of these papers, it is proved that there is a one-to-one correspondence between the set of all vague filters and all vague congruence of a lattice implication algebra. In another, the relations among fuzzy t-filters on residuated lattices are described. Another paper is devoted to the filter topology on lattice implication algebras. In further articles is characterized the relationship between the main types of fuzzy filters in BE-algebras and EQ-algebras. The role of ideals and soft sets in BL-algebras is described in another two papers. In papers on pseudo-weak-R0 algebras, the most simplified axioms system is presented and it is proved that pseudo-weak-R0 algebras are categorically isomorphic to pseudo-IMTL algebras. Pseudo-R0 algebras are categorically isomorphic to pseudo-NM algebras. Several presented papers are devoted to the possible applications of algebras inspired by logic and fuzzy sets. For example, a robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. A mathematical derivation is used to prove that the controller is able to achieve asymptotic stability by processing state measurements. Properties of some hesitant triangular fuzzy aggregation operators based on Bonferroni means also are discussed. In one paper, the method of a construction of a ranking of the physical matches is proposed. This method is based on the fuzzy clustering analysis. Decisions are often made by many decision experts having preference of risks. In view of the grey situation group decision-making problems, a grey situation group decision-making method on the basis of prospect theory is shown. The method takes the positive and negative ideal situation distance as reference points, defines positive and negative prospect value function, and introduces decision experts' risk preference into grey situation decision-making to make the final decision more in line with decision experts' psychological behavior. One possibility of determination of the weight of each decision expert sets up comprehensive prospect value matrix for decision experts' evaluation, and finally determination of the optimal situation is presented. Jianming Zhan Bijan Davvaz Wieslaw A. Dudek Young Bae Jun Hee Sik Kim

In this study, a fuzzy logic model was constituted by using the Fuzzy Logic (FL) method, which is one of the traditional artificial intelligence (AI) methods, in order to estimate the shear strength of reinforced concrete (RC) beams with limited ductility. In this model, beam width(bw), beam height(h), characteristic concrete compressive strength(fck), transverse reinforcement diameter(T), the number of arms bearing the shear force of the transverse reinforcement(n) and transverse reinforcement spacing(s) were taken into account as variable parameters. The model developed by using the problem data containing the solutions of shear force strength of 2640 beams with different cross-section properties were tested with 480 beam solutions different from these data. In the tests of the developed FL model, maximum percentage error, minimum percentage error, average percentage error and correlation coefficient values were obtained as 3.604, -0.091, 1.514 and R2=0.999678. By applying the fuzzy inverse logic method (FIL), which was recently developed by the author of this study, on the FL model, which is seen to have been developed quite sensitively from the test results, a total of 521 designs were obtained for 15 different RC beams with limited ductility subjected to shear. In order to check the accuracy of these designs, after shear strengths were obtained by conventional computations for these designs, % error and correlation coefficients were computed between the obtained strength values and the shear force values taken into account for the design. The promising results show that the FIL method can be used in the design of RC beams under shear force and even in other scientific studies such as design, optimization and control.

Fuzzy logic is a topic traditionally taught in artificial intelligence, machine learning, and robotics courses. Students receive the necessary mathematical and theoretical foundation in lecture format. The final learning experience may require that students create and code their own fuzzy logic application that solves a real world problem. This can be an issue when the target is a bioengineering course that introduces classical control theory, fuzzy logic, neural networks, genetic algorithms and genetic programming through the use of a low cost robot, personal digital assistant (PDA) handheld computer, and custom PDA software. In this course, the concepts and theories discussed in lecture are reinforced and extended in a corresponding laboratory through the use of wireless robots and PDAs. Fuzzy logic libraries and software modules for laptops and desktop computers are readily available, however, when it comes to handheld computers no such libraries exist. Students are able to spend more time experimenting with different fuzzy logic controllers when a custom fuzzy logic library and PDA graphical user interface are utilized. In this paper we introduce and discuss a unique low cost wireless robot, a custom fuzzy logic library, a custom fuzzy logic GUI for the PDA, and the implementation results for the fuzzy logic section in a newly created bioengineering course. Diagnostic and summative assessment in the form of a pre-test and post-test was administered for each section of the course, however, only the results for the fuzzy logic section will be provided.

Artificial intelligence and cognitive science must look at the world of industrial-process control to find the technological reifications of the concept of mind.

Human's can't imagine machines independent. From Vacuum Tubes technology to transistors and now with Integrated chip (IC), semiconductor technology defined another industrial revolution. The modern industrial twirl is already in transpire. Artificial intelligence (AI) is ushering in the new age of technologies that are super fast, more flexible, much potential, and initiating the world more digitally connected. No doubt the potential of IoT and AI to clean up the environment is cosmic. A computational concept like fuzzy logic, neural network, and machine learning will change the perspective of machine how they are used now. Our study reveals retrospect progression in the internet of things and artificial intelligence technologies to curb ecological pollution. New generation AI-enabled intelligent control systems are optimized with a complex algorithm to identify and eliminate pollutants for environmental clean-ups. With AI automation pollution management and mitigation, developments are examined. Adopting tech-savvy IoT and AI technology, dependency on machines can be seemly employed. For example; Transportation Management System using AI and IOT can be used to determine the best shipping routes by cutting fuel and gas consumption. To some extent ICT, wireless technology adds a contribution to reducing E-Waste. ICT together with IoT acts as a mediator while renting and sharing devices among people with different industries. AI helps to solve complex data analysis that supports Quick Decision System and policymaking. With intelligent robots, we can monitor and control acidification on Soil and water. The concept of neural network and fuzzy logic are greatly used to develop intelligent machines that predict different gas rates and chemical processes. AI machines that continuously check the pH level of water, Analysis Air Quality Index can be built to monitor water resources and atmosphere. Some AI robots can identify pollutants and helps to separate them. Now we are successful in a bifurcation of paper with plastic, Iron with aluminum. Such a method contributes to the waste management system appropriately. Our study also inspects the challenges of implementing AI, How data mining and big data management feed system.
 Authentication/Authorization work with industry and governing authority. Inspection of a biased algorithm, poor network, and security. There is no new route to achieve our goal. Our goal is to achieve paramount measures with two concepts in mind, that are Humans assist machines and Machines assist humans to control and prevent pollution in these critical situations. Both humans and machines together find an instant solution with renting and sharing that helps to minimize ecosystem effluence

It has been known for a few years that no more than Π11 ∆13 comprehension is needed for the proof of “Frege’s Theorem.” One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, Delta-3-1 comprehension axioms are not logical truths. What I suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called “ancestral logic” is developed, and it is then extended to yield what I call “Arché logic.”

Epistemic Logic and Information Update

The dynamics of spacecrafts with slewing payloads and flexible appendages are complicated, nonlinear, and coupling, which increase the difficulty of control. A new control scheme is presented for a type of flexible spacecrafts with slewing payloads. In the scheme, an adaptive fuzzy logic system (FLS) is designed to approximate the main dynamics of the plant, and an extended state observer (ESO) is introduced to observe and compensate the error of the FLS and quick-varying disturbances; at the same time, the output of the FLS is utilized to improve the performance of the ESO. The simulation results illustrate the effectiveness.

Human-computer interaction for virtual-real fusion

In healthcare sector, the people contemplate the best treatments and services notwithstanding of cost. Even if a huge amount of national budget disburses in this sector but it has not attained the society conjecture. Entire medical statistics are investigated by specialist. The complexities and the minutiae of the images and statistics can only be extrapolated by the specialists which escalate the workload and insistence of the specialists. The circumstances propagate to the need for the automated models for the healthcare systems. Artificial intelligence (AI) is a well-built domain of computer science which is attainable solution to all the real-world complications. Thus, AI can come up with exceptional and accurate solution with inordinate precision for medical imaging. Medical imaging embraces the identification, medicament and surveil the diseases in the particular images of medical fields like CT scan, X-rays, ultrasound images. AI methods can be employed to radiology, pathology, and dermatology for image processing. AI methods like deep neural networks, machine learning algorithms, fuzzy logic are some best solutions for image processing. In this paper, divergent AI techniques with their strength, limitations, and applications are delineate and the paper also provides a cognizance to contemporary approaches that attain optimum results in their respective domains. This paper concluded with the discussion of the barriers which reduced the growth of AI and the future opportunities of AI in the healthcare sector.KeywordsArtificial Intelligence (AI)Machine learningNeural networkFuzzy logicMedical imaging

Mathematical logic is a discipline used in sciences and humanities with different point of view. Although in tertiary level computer science education it has a solid place, it does not hold also for secondary level education. We present a heterogeneous study both theoretical based and empirically based which points out the key role of logic in computer science, computer science education and knowledge representation. We focus on the key contrast of semantics and syntax, the resolution principle as a leading inference technique (giving also interesting non-clausal generalization of the rule). Further we discuss the possibilities of inclusion the non-classical (many-valued) logics in education together with the original generalization of the non-clausal resolution rule into fuzzy logic. The last part describes partial results of the research concerning the secondary education in the Czech Republic especially in the mathematical logic field. The generalization of the presented ideas entails the article.

The protection of sensitive facilities or international borders using Wireless Sensor Networks (WSN) has become one of the important topics nowadays. One of the efficient techniques which could guarantee a high precision capabilities of event detection is to depend on Fuzzy Logic System (FLS) as the Artificial Intelligence(AI)-based processing algorithm, in addition to use the Field Programmable Logic Array (FPGA) as the hardware platform due to its reconfigurability and high-speed processing power that it could provide. In this paper, we designed a systolic-based FLS architecture using VHDL based on the validated MATLAB model. The proposed systolic FLS architecture has been designed to be interfaced with a TFmini Plus Lidar Sensor Lidar sensor and a MaxSonar ultrasonic sensor using the Intel Altera OpenVINO FPGA kit. The proposed systolic FLS processing core achieved a processing computational speed of 3.085 GOPS at maximum operating frequency of 181.55 MHz, while draining only 29.09 mW as a core dynamic thermal power dissipation loss and only about 12.98 mW as a I/O thermal power dissipation loss.

We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Morleyization in this framework are discussed and some natural examples of fuzzy theories are presented. ajek and Cintula wrote: \In the last few decades many formal systems of fuzzy logics have been developed. Since the main dierences between fuzzy and classical logics lie at propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this paper we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate In that paper the authors proved a generalized completeness result for a wide class of fuzzy predicate logics, namely core fuzzy logics. To do this they used a generalized Henkin method for a through survey of the present status of fuzzy predicate logic, see (3). In the present paper we continue the work on fuzzy predicate logics by developing further model theory of these logics. We choose Lukasiewicz predicate logic. The reason is that the Lukasiewicz BL-algebra is equipped with continuous operations and this is essential in proving the compactness theorem which is a fundamental result in model theory. Here, the compactness theorem says that if each nite subset of a set of sentences has a Lukasiewicz model, then the set itself has a Lukasiewicz model. As consequences of compactness, we prove the most basic model theoretic results including the upward and downward Lowenheim-Skolem theorems. We also prove suitable versions of the most well known preservation theorems, including preservation theorems for universal and inductive theories. At the end, we introduce some fuzzy theories and study their model theoretic properties. To prove the compactness theorem, we use ultraproduct and its basic properties which we rst investigate. We follow the old methods developed by Chang and