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'Logic and Its Applications Ramanujam R. Sundar Sarukkai (Articles)'

'Logic and Its Applications Ramanujam R. Sundar Sarukkai (Articles)'

Book digitized by Google from the library of the University of Wisconsin - Madison and uploaded to the Internet Archive by user tpb.

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this purpose are various clones over a full subcategory of a category. We show that the syntax of equational logic, lambda calculus and first order logic can be represented as clones or right algebras of clones over the set of positive integers. The semantics is then represented by structures derived from left algebras of these clones.

Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program against a specification is transformed equivalently into an order relation between matrices. Due to the limitation of Isabelle/HOL, the calculation of the order relation is solved by calling an outside oracle written in Python. To the best of our knowledge, this is the first theorem prover for quantum programs. To demonstrate its power, the correctness of two well-known quantum algorithms, i.e., Grover Quantum Search and Quantum Phase Estimation (the key step in Shor's quantum algorithm of factoring in polynomial time) are proved using the theorem prover. These are the first mechanized proofs for both of them.

Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program against a specification is transformed equivalently into an order relation between matrices. Due to the limitation of Isabelle/HOL, the calculation of the order relation is solved by calling an outside oracle written in Python. To the best of our knowledge, this is the first theorem prover for quantum programs. To demonstrate its power, the correctness of two well-known quantum algorithms, i.e., Grover Quantum Search and Quantum Phase Estimation (the key step in Shor's quantum algorithm of factoring in polynomial time) are proved using the theorem prover. These are the first mechanized proofs for both of them.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n symbol or numerical valued refined neutrosophic logic. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively

A fuzzy syllogism in fuzzy logic is defined in this paper to be an inference schema in which the major premise, the minor premise and the conclusion are propositions containing fuzzy quantifiers. This paper may be viewed as an initiation of a study of syllogistic reasoning in the context of fuzzy logic. Such reasoning has a direct bearing on the rules of combination of evidence in expert systems and, in addition, provides a basis for inference from commonsense knowledge by viewing such knowledge as a collection of dispositions. The results presented in this paper are preliminary in nature. The issue of syllogistic reasoning in fuzzy logic has many ramifications which remain to be explored.

A fuzzy syllogism in fuzzy logic is defined in this paper to be an inference schema in which the major premise, the minor premise and the conclusion are propositions containing fuzzy quantifiers. This paper may be viewed as an initiation of a study of syllogistic reasoning in the context of fuzzy logic. Such reasoning has a direct bearing on the rules of combination of evidence in expert systems and, in addition, provides a basis for inference from commonsense knowledge by viewing such knowledge as a collection of dispositions. The results presented in this paper are preliminary in nature. The issue of syllogistic reasoning in fuzzy logic has many ramifications which remain to be explored.

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that incorporates a contextual transformation function, enabling the adjustment of logical connectives in conjunction with flipping truth values based on contextual shifts. Furthermore, the paper introduces Indeterm-Upside-Down Logic and Certain Upside-Down Logic, both of which expand Upside-Down Logic to better accommodate indeterminate values. Finally, a simple algorithm leveraging Upside-Down Logic is proposed and analyzed, providing insights into its computational characteristics and potential applications.

Book digitized by Google from the library of the University of California and uploaded to the Internet Archive by user tpb.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general nsymbol or numerical valued refined neutrosophic logic. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general nsymbol or numerical valued refined neutrosophic logic. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively

xi, [1], 141, [1] p. :

The idea of fuzzy logic is based close to the human reasoning and regular exercises. It presents predicates which are available in nature and like those either enormous or little. This hypothesis copies human brain science in the matter of how a man settles on the choice speedier. Fuzzy logic is a superset of ordinary (Boolean) logic that has been stretched out to deal with the idea of halfway truth - truth esteems between "totally obvious" and "totally false". It can be actualized in equipment, programming, or a mix of both. It can be incorporated with anything from little, hand-held items to vast modernized process control frameworks.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valuedlogic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophicconorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined Neutrosopjhic Probability.

The idea of fuzzy logic is based close to the human reasoning and regular exercises. It presents predicates which are available in nature and like those either enormous or little. This hypothesis copies human brain science in the matter of how a man settles on the choice speedier. Fuzzy logic is a superset of ordinary (Boolean) logic that has been stretched out to deal with the idea of halfway truth - truth esteems between "totally obvious" and "totally false". It can be actualized in equipment, programming, or a mix of both. It can be incorporated with anything from little, hand-held items to vast modernized process control frameworks. Deepak Sharma | Sohan Garg"A critical study of fuzzy logic systems and its applications" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-1 , December 2016, URL: http://www.ijtsrd.com/papers/ijtsrd105.pdf Article URL: http://www.ijtsrd.com/engineering/computer-engineering/105/a-critical-study-of-fuzzy-logic-systems-and-its-applications/deepak-sharma

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic.

xi, 141 p. 23 cm

xi, 141 p. 23 cm

xi, 141 p. 23 cm

xi, 141 p. 23 cm

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined Neutrosophic Probability.

Introduction to Symbolic Logic

The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., VeryTrue, VeryProbablyTrue, and LittleFalse, taken from a hedge algebra of a linguistic truth variable, and linguistic hedges (modifiers) can be used as unary connectives in formulae. This is motivated by the fact that humans reason mostly in terms of linguistic terms rather than in terms of numbers, and linguistic hedges are often used in natural languages to express different levels of emphasis. The paper presents: (i) the language of fuzzy linguistic logic programming; (ii) a declarative semantics in terms of Herbrand interpretations and models; (iii) a procedural semantics which directly manipulates linguistic terms to compute a lower bound to the truth value of a query, and proves its soundness; (iv) a fixpoint semantics of logic programs, and based on it, proves the completeness of the procedural semantics; (v) several applications of fuzzy linguistic logic programming; and (vi) an idea of implementing a system to execute fuzzy linguistic logic programs.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined Neutrosopjhic Probability.

The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful transformations in logics of knowledge (e.g., to support multi-agent planning with knowledge actions and degrees of visibility) have been proposed. This paper explores the use of logic programming (LP) to encode interesting forms of logics of knowledge and compute Kripke models. The LP modeling is expanded with useful operators on Kripke structures, to support multi-agent planning in the presence of both world-altering and knowledge actions. This results in the first ever implementation of a planner for this type of complex multi-agent domains.

The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful transformations in logics of knowledge (e.g., to support multi-agent planning with knowledge actions and degrees of visibility) have been proposed. This paper explores the use of logic programming (LP) to encode interesting forms of logics of knowledge and compute Kripke models. The LP modeling is expanded with useful operators on Kripke structures, to support multi-agent planning in the presence of both world-altering and knowledge actions. This results in the first ever implementation of a planner for this type of complex multi-agent domains.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined Neutrosophic Probability.

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutrosophic logic. Two classes of neutrosophic norm (n-norm) and neutrosophic conorm (n-conorm) are defined. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined Neutrosophic Probability.

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