Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

A Fuzzy Petri Nets Model for Computing With Words

Motivated by Zadeh's paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, Petri nets, together with fuzzy set theory and thereby establish a concurrency model of computing with words--fuzzy Petri nets for computing with words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which makes it possible for computing with more words. The language expressiveness of the two formal models of computing with words, fuzzy automata for computing with words and FPNCWs, is compared as well. A few small examples are provided to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure

Robotic Behavior based on Formal Grammars

Formal grammars, studied by N. Chomsky for the definition of equivalence with languages and models of computing, have been a useful tool in the development of compilers, programming languages, natural language processing, automata theory, etc. The words or symbols of these formal languages can denote deduced actions that correspond to specific behaviors of a robotic entity or agent that interacts with an environment. The primary objective of this paper pretend to represent and generate simple behaviors of artificial agents. Reinforcement learning techniques, grammars, and languages, as defined based on the model of the proposed system were applied to the typical case of the ideal route on the problem of artificial ant. The application of such techniques proofs the viability of building robots that might learn through interaction with the environment

Analogical study of Support Vector Machine (SVM) and Neural Network in Vehicleas Number Plate Detection

Formal grammars, studied by N. Chomsky for the definition of equivalence with languages and models of computing, have been a useful tool in the development of compilers, programming languages, natural language processing, automata theory, etc. The words or symbols of these formal languages can denote deduced actions that correspond to specific behaviors of a robotic entity or agent that interacts with an environment. The primary objective of this paper pretend to represent and generate simple behaviors of artificial agents. Reinforcement learning techniques, grammars, and languages, as defined based on the model of the proposed system were applied to the typical case of the ideal route on the problem of artificial ant. The application of such techniques proofs the viability of building robots that might learn through interaction with the environment

Эпистемическая модальная логика, универсальная философская эпистемо-логия и естественная теология: всеведение Бога как формально-аксиологический закон двузначной алгебры метафизики как формальной аксиологии (Обоснование этого закона "вычислением" соответствующих ценностных функций)

The method of constructing and investigating discrete mathematical models is applied to the problem of Omniscience-by-God, which is located at the intersection of epistemology, theol-ogy, and epistemic logic. For the first time in epistemology and philosophical theology, the tenet of God’s Omniscience is formulated by the artificial language of two-valued algebra of metaphysics as formal axiology, and demonstrated as a formal-axiological law of that alge-bra by “computing” relevant evaluation-functions. The present article continues the author’s attempts to apply the conceptual apparatus and meth-ods of discrete mathematics to analytical theology, namely, to represent and solve difficult problems of philosophical theology by means of constructing and investigating their models at the level of artificial language of two-valued algebraic system of metaphysics as formal axiology. The author has already published a paper on discrete mathematical modeling the tenet of God’s omnipotence in [Tomsk State University Journal of Philosophy, Sociology and Political Science. 2019. Vol. 47. P. 87–93]. In com-parison with the mentioned paper, the present article submits significantly new scientific results of constructing and investigating a discrete mathematical model of another famous attribute of God, namely, of His omniscience. In contrast to the tenet of God’s omnipotence affirming that He is al-mighty, the tenet of God’s omniscience affirms that He knows everything. However, the literature on philosophical theology contains indicating and discussing a set of nontrivial logical and epistemologi-cal problems concerning All-Knowing-God. Just these problems (and solving them at the level of their mathematical model) make up the subject-matter of the given article. The paper starts with explicating a formal-axiological meaning of the statement “God knows everything” by explicating formal-axiological meanings of the words “God”, “knows”, and “thing”. In particular, it is emphasized that the word “knowledge” is a homonym possessing at least three qualitatively different meanings, namely, “a-priori knowledge”, “empirical knowledge”, and knowledge-in-general”. It is demonstrated that God’s knowledge is not empirical but a-priori one. All the formal-axiological meanings under discus-sion are considered as evaluation-functions and defined precisely by tables. Significantly new scien-tific result of the present article: for the first time in the world literature on philosophical theology, the tenet of All-Knowing God is precisely formulated by means of the artificial language of two-valued algebra of metaphysics as formal axiology, and proved as a formal-axiological law in this algebra by computing relevant evaluation-tables. The hitherto never published affirming God’s omniscience as the law of two-valued algebra of metaphysics as formal axiology is quite nontrivial and psychological-ly unexpected one, although from the viewpoint of mathematics proper, its proof is simple

A (Truly) Local Broadcast Layer for Unreliable Radio Networks

In this paper, we implement an efficient local broadcast service for the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Our local broadcast service offers probabilistic latency guarantees for: (1) message delivery to all reliable neighbors (i.e., neighbors connected by reliable links), and (2) receiving some message when one or more reliable neighbors are broadcasting. This service significantly simplifies the design and analysis of algorithms for the otherwise challenging dual graph model. To this end, we also note that our solution can be interpreted as an implementation of the abstract MAC layer specification---therefore translating the growing corpus of algorithmic results studied on top of this layer to the dual graph model. At the core of our service is a seed agreement routine which enables nodes in the network to achieve "good enough" coordination to overcome the difficulties of unpredictable link behavior. Because this routine has potential application to other problems in this setting, we capture it with a formal specification---simplifying its reuse in other algorithms. Finally, we note that in a break from much work on distributed radio network algorithms, our problem definitions (including error bounds), implementation, and analysis do not depend on global network parameters such as the network size, a goal which required new analysis techniques. We argue that breaking the dependence of these algorithms on global parameters makes more sense and aligns better with the rise of ubiquitous computing, where devices will be increasingly working locally in an otherwise massive network. Our push for locality, in other words, is a contribution independent of the specific radio network model and problem studied here