We study three kinds of compactness in some variants of Godel Logic: compactness, entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkin construction to prove the compactness property of extensions of first-order Godel Logic enriched by nullary connective or the Baaz's projection connective.In the case of uncountable first-order language we use the ultraproduct method to derive the compactness theorem.

The question as to whether the propositional Logic of Heyting, which was a formalization of Brouwer's intuitionistic Logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gö del (1932) introduced an infinite decreasing chain of intermediate Logics, which are known nowadays as Gö del Logics, for showing that the intuitionistic Logic is not finitely (many) valued. Now we know that the propositional intuitionistic Logic is infinitely many valued (with a countably many Logical values). In this paper we provide another proof for this result of Gö del, from the perspective of Kripke model theory. Š vejadr and Bendova (2000) proved that in Gö del fuzzy Logic the conjunction and implication are not definable by the rest of the propositional connectives (while disjunction is definable by conjunction and implication). In this paper, we show that disjunction is not definable by implication and negation in Gö del fuzzy Logic; two proofs, one by Kripke models and one by fuzzy semantics, are provided for this new theorem.

Usually two-dimensional substitution is used for the production of integrated circuits. Due to heavy use of communications, two-dimensional substitution has high losses as well as, density of elements is low in it. To resolve this problem, three-dimensional substitution method was proposed. Rather than the two-dimensional arrangement of elements in a row, elements are layout in three dimensions in this substitution. In this paper, three-dimensional substitution algorithms using order used in two-dimensional substitution, three-dimensional substitution analysis by mPL and three-dimensional substitution simultaneous with two-dimensional substitution by mPL have been studied in terms of structure and function, and a butterfly processing element (PE) and an Advanced Encryption Standard (AES) block and a wireless MIMO decoder to assess them have been implemented with the mentioned methods. . Applying these methods shows that the use of face to face integration by microbuses in communications of substitution algorithm, on average, improves the maximum clock and block speed of AES encryption to 15. 3% and the maximum clock and block speed of PE module to 22. 6% as well as the maximum clock and speed of MIMO modules to 17. 1%, while the use of these methods has led to the average reduction in power consumption of 2. 6% for the AES module and the average reduction in power of 12. 9% for the PE module and the average reduction in power consumption of 5. 1% for MIMO module.

Einstein’s theory of relativity made many difficulties for Newtonian physics, so as it did not remain any way for keepingit but setting apart or reforming some of the most fundamental concepts such as space and time. Many thinkers believe that relativity theory made some irreparable hurts on Kant’s philosophy. However, some other thinkers, like Godel, have tried to read relativity theory in such a way that not only have no contradiction with Kant’s philosophy, but also introduce some affirmations for it. This paper casts light on Godel’s effort for reconciling relativity theory with Kant’s philosophy in the topic of ' Time'; It also contains some remarks on the point that how conception of time in relativity theory can lead us to defend Idealism. Finally, it would be suggested that for reconciling Kant’s philosophy with modern science, we should both cease his inflexibility about the process of acquiring knowledge and set apart the hypothesis of being unknowable of the thing-in-itself.

We know for Logic two systems: the Ancient Logic and the Modern Logic, which are inconsistent in some points of view. In this paper, I want to see if Ancient Logic, versus Modern Logic, is really one Logic, has one set of rules, and introduces one methodology. There are many disagreements on the number and the exact formulation of the valid rules of Ancient Predicate Logic. For instance, the various formulations of the Obversion and Contraposition (the congruent and the opposite) can be mentioned as evidence for the claim. Since Aristotle has not spoken of contraposition, it can be concluded that adding the two forms of contraposition to his Logical rules provide us with two new Logical systems, in which the formulations of the quantified propositions differ from that in Aristotle’s system. Also, since there have appeared different theories on Congruent Contraposition and the Obvertion between Muslim Logicians, the number of the systems has reached the six. In this paper, introducing an exact definition for each of these systems, I present suitable formulations for the quantified propositions at the mentioned six systems.

Quantum mechanics replaced the traditional mechanics in the early twentieth century. To study Schrodinger’ s wave equation, whose position in this new mechanics is like the status of Newton’ s movement laws in traditional mechanics, numerous philosophical statements have been offered, one of which is ‘ quantum Logic’ . The founders of quantum Logic claim that on the basis of their observations in quantum level, the traditional Logic, which previously served as the measurement for right and wrong arguments, lacks the proper efficiency and must be replaced by one of the expressions of quantum Logic. In the present article, while shortly introducing quantum mechanics and quantum Logic, we have avoided entering the formal discussions of quantum Logic and used analytical method to investigate the possibility of replacing the traditional Logic with quantum Logic. According to this study, it was clarified that one must regard quantum Logic just as a mathematical formulization, not an alternative Logic, because firstly it is dependent on a certain statement of Schrodinger’ s equation, and secondly, one must use traditional Logic to falsify it. Applying this Logic to traditional and quantum Logic would result in truth and falsehood of both Logics and not falsehood of traditional Logic and truth of alternative Logic.

In 1970, Gödel showed his ontoLogical argument to Dana Scott and discussed it with him. Afterwards, Scott presented a slightly different version of the argument at Princeton University. The Logical system of the argument is a second-order quantified S5-modal Logic with identity and an abstraction operator. Granted the acceptability of the underlying Logical system, Godels conclusion that necessarily there exists a God-like being) can be derived from the premises-with Godel and Scott on the scene, who can say otherwise? Sobel, however, proved that the system faces modal collapse-i.e. P↔ðP is derivable from the system. Responding to Sobel, Anderson tried to block this by weakening some axioms and definitions.In this paper, I will be trying to consider Godels ontoLogical argument (Scotts version) from a Logical point of view, along with Sobels criticism and Andersons emendations.

When hearing the term fuzzy Logic, the first thing that the mind immediately goes to is the field of non-deterministic arguments, and if we want to use a term close to it to make its meaning a little clearer, we can say that fuzzy Logic is the same as Armagon's Logic. It is an approximation that, ironically, the literal meaning of the word "argument" also refers to the clarification of something by the same thing (function input or armagon). Now the basic question is that while the educated mind of man has considered Logic as equivalent to the mechanism of definite perceptions and accurate results for more than a thousand years, how can we talk about the invention of a Logical method that is based on uncertainty? This question is doubly important from the aspect that our approximate arguments in the context of our lived life are more than our exact, definite and unambiguous arguments, that is, the same arguments that classical Logic, whether in its old or new language, He leaves it aside and does not pay attention to them, and of course he is forced to do this because he does not have the tools to analyze these arguments. This is where we unknowingly remind ourselves of Bacon's angry regret, who considers Aristotelian Logic to be a fantasy that causes waste and diversion of great talents over many centuries, a continuous and constant effort without helping a person to improve the quality of his life; A bunch of delusional nonsense, the result of which, perhaps in the most optimistic state, is Scott's adversary and the victory of futility in verbal disputes, of course, if we do not say only pointless boasting and scrutiny based on rhetoric, the fruit of which is the explanation of rational axioms. If Mr. Bacon knew about fuzzy Logic, he would have corrected his view of Logic, and to be more precise, he would have separated Aristotle from Logic, not Logic from science. One of the most important advantages of fuzzy Logic is that it can introduce a way to enter the knowledge and experiences of experts into intelligent systems that are based on sensitive and practical decisions and choices and develop the previous absolute correct and incorrect Logic. The basis of the analysis in the present research is to examine the components of two types of Logic, i.e. classical Logic and fuzzy Logic, and clarify the understanding of the Logical concepts and philosophical foundations of classical Logic, as well as comparing it with the concepts of fuzzy Logic. The research results indicate: these two types of Logic have fundamental differences from an epistemoLogical point of view; Aristotle's epistemoLogical foundation is based on the certainty-oriented duality of "either this/or that", while the fuzzy epistemoLogical foundation is based on a multi-valued system and that both Logics are a contradictory understanding of what the mind and the external world are and the connection between They both give hands.

Continuous Logic is generalization of first order Logic to a many valued Logic with an infinitary truth value set. Many of the results of classic Logic and it's model theory have been generalized to continuous Logic. Continuous Logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of continuous Logic from Ł ukasiewicz Logic. Then we have a review on some of the most important basic results of continuous Logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of continuous Logic that is based on continuous t-norm based fuzzy Logics. This will lead to the introduction of two kinds of continuous Logics based on Gö del Logic and product Logic. Then we developed some of the results of continuous Logic suContinuous Logic is generalization of first order Logic to a many valued Logic with an infinitary truth value set. Many of the results of classic Logic and it's model theory have been generalized to continuous Logic. Continuous Logic not only has many uses in the mathematical analysis and in the model theory of mathematical analysis structures, but also has created new attitudes in classical model theory. Firstly, the present paper study the development of continuous Logic from Ł ukasiewicz Logic. Then we have a review on some of the most important basic results of continuous Logic, including the completeness of the proof system and the compactness theorem. Finally, according to the concept of continuity with respect to the truth value set, we will introduce a kind of continuous Logic that is based on continuous t-norm based fuzzy Logics. This will lead to the introduction of two kinds of continuous Logics based on Gö del Logic and product Logic. Then we developed some of the results of continuous Logic such as the compactness theorem for these two Logics. h as the compactness theorem for these two Logics.