Sharif Digital Repository

Nowadays, BDI architecture is of the most well known agent’s architectures. BDI architecture or the architecture in which the system is viewed as rational agents based on the attitudes of belief, desire and intention represents an abstraction of human deliberation based on a theory of rational action in the human cognition process. BDI logic introduced by Rao and Georgeff have been widely used as the theoretical basis of specification and implementation of rational agents. BDI logic is limited to deal with crisp assertion, while the assertions encountered in real world are not precise and thus cannot be treated simply by using yes or no. Moreover, In order to obtain more human like agents we... 

Pregroups as a mathematical structure, are replacement for Lambek's type caregorial grammar which much used in Computational Linguistics. Because of computational and logical properties of pregroups, we can use them as strong tool to analyse the sentence structure of many natural languages. This kind of analysis has been done for English, French, German, Polish, Italian, Arabic and Japanese. In case of Persian language, analysis of simple and compound sentences structure with simple tense verbs and explicit subjects and objects has been studied. In this M.Sc. thesis, we will extent analysis of Persian sentence structure to sentences with compound tense verbs and implicit subjects and objects... 

Description logic is a family of knowledge representive languages which represents knowledge via propositional logic (first order logic) propositions and constructors and applies its services for reasoning and consistency checking. Nowadays description logic and its popular reasoner FaCT++ which applies tablue reasoning technique are widely used in applications such as semantic web and onthologies. Model checking is a technique for systems and models verification and to guarantee the accuracy of design. Given a model description and a specification formula, the model checker verifies the model against the specification and decides if the model satisfies the description or not. Main model... 

Deontic logic is used to formalize legal reasoning. To apply this logic in law, we describe tersely some efforts to improve this logic by relativizing its operations with respect to different people and groups of society. Until now, this logic was restricted to formalize “what must be”. We extend this logic to dyadic logic to formalize “what must be done”.
In practice, legal reasoning leads to non-monotonic logics, the most applicable one in law is defeasible logic. So it is necessary to combine deontic and defeasible logics to formalize legal reasoning in a more appropriate way. To do that, we must adjust possible worlds of these two logics. In this way, we find a method for... 

In this dissertation, we study (first-order) arithmetical interpretations for propositional (modal and non-modal) logics. More precisely, the following results are included in this dissertation: an axiomatization for provability logic of Heyting Arithmetic, HA, and its self-completion HA := HA + PrHA(⌜A⌝) ! A for 1-substitutions is provided, and their arithmetical completeness theorems are proved. We also show that they are decidable. The de Jongh property for Basic Arithmetic BA, HA and HA + □ are proved  

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... 

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... 

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... 

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... 

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  

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)  

In constructive mathematics, one has to construct a mathematical object in order to show that it exists. Consequently, some of classical theorems are not acceptable from a constructive point of view. In particular, the constructive validity of the parts of mathematics that play a role in forming physical theories is of interest. Here, we want to examine the constructive provability of some theorems related to quantum mechanics  

Automatic theorem proving has been attractive in artificial intelligence (AI). The aim of the usual automatic theorem proving methods is applying of the mathematical logic rules to decide intelligently, and reasoning automatically. In contrast the aim of our research is to apply computers abilities and artificial intelligence methods to simulate human abilities to prove mathematical theorems. For this purpose, we invent a typed formal language (TFL) to describe mathematical theories. The language must be clearly computable and should cover the First Order Logic (FOL) and the usual mathematical sentences. Then some algorithms and inference rules to compare sentences conceptually are... 

In this thesis, we investigate constructive measure theory in two schools of constructivism; intuitionistic mathematics and Bishop’s constructive mathematics.In this regard, first, we examine some classical propositions on measurability in both schools. Then we give a comparison between measurability in the two schools  

Epistemic algorithms are instructions and rules based on knowledge of agents. These algorithms by individual or group knowledge of agents make decisions about future behavior of systems. Epistemic gossip protocols is one of these algorithms. They are used to for spreading secrets among nodes in a network. According to individual knowledge of each node they decide who calls whom in each step. In security problems epistemic algorithms are used to detect the safety of protocols. Some epistemic notions like ignorance and contingency are used in formalization of security problems. In the thesis we study these epistemic algorithms  

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... 

In 1933, Gödel’s paper “An interpretation of the intuitionistic propositional calculus”[12] introduced a proof interpretation of the intuitionistic propositional logic to the modal system, S4, which interprets the logical constant as a provability predicate. Fortunately, this interpretation has the soundness-completeness property and therefore we can prove the constructivist’s viewpoint which states that the intuitionistic truth and provability are identical. However, there is a mathematical trick in his work. In fact, Gödel used a proof theory of the concept of proof instead of an explicit interpretation. Furtheremore, he proved the failure of any interpretation of this implicit proof as a... 

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, we study recursion theory in the context of Bishop’s constructive mathematics.For this goal, at first, we redefine primitive recursive functions and then based on works of Fred Richman in [Church’s Thesis Without Tears, The Journal of Symbolic Logic, Vol. 48, No. 3 (Sep., 1983), pp. 797-803], give an interpretation of partial recursive functions. Finally we study some important theorems in recursion theory,for example, universal computation predicate, recursion theorem, s-m-n theorem and
Rice’s theorem