Sharif Digital Repository

In this thesis we construct a bounded translation of intuitionistic predicate logic into Basic predicate logic with restricted use of universal quantifier and without equality inspired by papers [1] and [2]  

With development of power electronic science and with the existence of different power electronic converters in this field, the need for improving their operation and the fault detection methods of these converters, the need for simulation and test of them is strong felt. However, experimental constrain such as damage risks, reliability, costs, and so on obviate the need for making the converter and the need for testing it and its controller. Accordingly, we do the testing on a special platform for Real-Time simulation.Control/protection platform needs to be tested and its functionality should be verified prior to installation and commissioning.Testing in theReal-Time simulator environment... 

Governments use tariff and non-tariff import barriers for several reasons including protecting national industries, tax income and or checking the quality of imported products. These barriers motivate importers to make a profit through smuggling. This study focuses on “import tariff rate” as a main motivation for smuggling and tries to estimate the elasticity of smuggling with respect to tariff rates. Iran trade flow data and tariff rates are collected from Trademap, WITS, Iran’s customs administration and Iran’s Trade Development Organization. By observing reported exports to Iran from main trade partners together with reported imports to Iran we construct a proxy for the amount of... 

IF Logic is an extension of First-Order logic, including syntactic connective ’/’ (independence indicator) which carries the concept of ’independent from’ in language and metalanguage.This logic which has introduced by Hintikka and Sandu in 1989, uses Game-theoretical semantics (GTS) such that every formula is defined as a game and the players are verifier and falsifier of its truth. The formula is True if the verifier has a winning-strategy and it is False where the falsifier has a winning-strategy; and evaluated as indeterminate otherwise. this relates a central concept of logic (truth) to a central concept of game theory(winningstrategy)  

Arising from the intersection of two modern ideas in logic and mathematics, namely Type Theory - specifically Martin-Löf’s intuitionistic type theory, and Homotopy Theory, Homotopy Type Theory has introduced a novel formalism that formalizes every mathematical object - including constructions, definitions, and proofs - in a specific and fundamentally different way from other interpretive frameworks (such as set theory), bringing forth new results - both philosophically and mathematically. The first goal of this research is to understand the meaning of Homotopy Type Theory as a foundation for mathematics through exploring this new formalism. The second goal of this research is to understand... 

The verification of programs is one of the most important subjects in Computer Science. In this thesis, after reviewing preliminary subjects, While-Programming computational model is presented and its semantics is discussed. Next, the axiomatic method of Hoare is presented, which is a deduction system for verification of programs. With the help of Hoare method, the idea of Data-Oriented verification of programs is developed  

In this thesis the sequent calculi for intuitionistic logic have been studied and compared with these calculi in classical logic, moreover soundness and completeness theorems for these calculi have been proved. Also an algorithmic method is presented to construct the proof-search with this feature that proof-search terminates and the subformula property preserved. In particular the analysis and comparison of two calculi IG and SIC provided by Tassi and Corsi have been done. Finally, we consider the calculus SJC, stack-based Jankov calculus which is similar to SIC and describes proof-search procedure for weak excluded middle logic. If the proof-search is successful in each calculus SIC or... 

The epistemic program in game theory uses formal models of interactive reasoning to provide foundations for various game-theoretic solution concepts. Much of this work is based on the (static) Aumann Partial models of interactive epistemology, but more recently dynamic models of interactive reasoning have been developed to analyse rational play in extensive form games. Here we surveyed (static) Aumman Partial models and (dynamic) Baltag and Smets plausibility models. compared these models, And investigated the backward induction problem by using these models  

One of the the most fundamental questions in computability (recursion) theory is the exact structure of D and in particular that of R. Over the years, various efforts have eventuated in Degree ?eory, an interesting subfield of computability theory, which is concerned with various properties of these algebraic structures which have turned out to be extremely complex. Beyond any doubt, the most useful tool for proving theorems related toRis the Priority Method which is first introduced to solve the Post’s problem. Over the years, increasingly more sophisticated versions of the method have been used to prove complex statements about R. Roughly one may classify the priority arguments into three... 

Epistemic logic gets its start with the recognition of the systematic properties of epistemic concepts. These properties make epistemic concepts amenable for formal study, and become our tools to present logical models for them.“Certainty” is one of these epistemic concepts for which no comprehensive logical model has been presented so far.
Among the logical models that have been presented for “Certainty”, there are two main models which are more comprehensive than the others and all the other models may be extendable to one of them. In this thesis, these two main logical models that have been proposed for the concept of certainty are introduced and described from a philosophical... 

Provability Logic is the study of Peano Arithmetic from the point of provability. The ◻ of modal logic is interpreted as ”Provable in PA ”. Gödel’s technique of proof, in his incompleteness theorems, showed that meta-lingual sentences such as ”A is provable in PA ” can be expressed by sentences of object language. Studying provability in the system K4 will lead us to a soundness theorem but in 1976, Robert Solovay showed that if we add an axiom -known as Löb’s axiom- to the system K4, we will have a completeness theorem as well. So GL = K4 + Löb is the provability logic of PA. In this thesis we will study these theorems  

One of the most important variants of classical logic is intuitionistic logic, which has arisen from the contemporary studies in the foundation of mathematics. Suppose we want to investigate the foundation of mathematics from a constructive point of view. For this purpose, we can choose two different ways. The first one is to modify the classical set theory, ZFC, in a way that is valid from a constructive point of view and is enough to formulate constructive mathematics, as well. The second approach, which is somehow different from the first one, is a foundational and dependent codification of the same foundation in a way that completely reflects constructive views.In this work we will... 

A data transmission network constitutes of finite number of data processing stations which are connected together through data transmission lines. Each data transmission network corresponds to a graph which is called network’s graph. Obviously there are meaningful relations between structural properties of network’s graph and efficiency of network. In this thesis we investigate two aspects of network’s graph. The first subject is Cayley graphs. It has been shown that Cayley graphs are good models for designing data transmission networks. In this thesis we have surveyed some structural properties of Cayley graphs. The second subject is isoperimetric number. The isoperimetric number is a good...