The second order logic is a part of classical logic whose vocabulary is made by adding predicate Variable to the vocabulary of the first order logic (without identity). Hence, the formation rules, the axioms and the rules of inference in this logic are made according to the first order logic (without identity).The axioms of this logic consists of the axiom schema of the first order logic (without identity), some axioms similar to the axioms of first order logic, and axiom schema of Relation comprehension and function comprehension. In this logic, the axiom of identity can be established by the Leibnitian definition of identity.Two semantics are presented for the second order logic: Standard semantics whose models resemble the ordinary models of the first order logic, and Henkin semantics which is distinct From standard semantics by its ability of limiting sets.Any valid formula in Henkin model is valid in standard model, not vice versa. And each Satisfiable formula in standard semantics is also satisfiable in Henkin semantics, not vice versa.The axiom of relation comprehension is not valid in Henkin semantics. The Soundness and Consistency metatheorems of the second order logic can be proved in both Henkin semantics and Standard semantics. We can prove the inCompleteness and the incompactness metatheorems of the second order logic by standard semantics. But in Henkin semantics, the Completeness and compactness metatheorems of the second order logic can be proved.In this article, the main aim is studying-the significance of semantic changing and its Consequences in syntax (axioms, ways of inferences,…) and in metatheorem by concentrating on second order logic. We have shown that the change in semantics will result in changes in the abovementioned parts.

In other articles, we have examined Mortaza Hajhosseini's natural deduction systems as presented in the second edition of his book, "Two Non-Classical Logic Systems: A New Outlook on Elements of Logic." In this article, our focus shifts to the semantics of these systems and an analysis of the issues surrounding Soundness and Completeness, as proven by Hajhosseini. We find that the book lacks clear definitions or definite specifications for several semantical terms used, including 'world,' 'supposed,' 'supposible,' 'basic situation,' and 'basic model.' Consequently, the semantic concepts of "validity" and "truth-preserving" in this context can be subject to multiple interpretations, some of which render certain relevant inferences irrelevant while others deem irrelevant inferences valid.Furthermore, we demonstrate that this semantics framework is incompatible with the proof theory presented in the book. The Meta-Theorems of Soundness and Completeness, as formulated, are erroneous and can be refuted with counterexamples. For instance, within the truth-functional system's semantics outlined in the book, a logical truth implies any other logical truth. However, the proofs provided in the book's natural deduction system are deemed 'invalid' because they violate Dag Prawitz's "normality" condition.

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining probabilistic metric spaces. Then the Dirac function is presented as an important example of distributions functions. We also, introduced Sibley’ s metric or Levy metric on the set of distance distribution functions and so this space becomes a metric space. In the following, probabilistic metric spaces are defined from the Serstnev’ s view, and some examples such as Menger probabilistic metric spaces, are introduced. In this paper, the strong topology induced by distance distribution functions is introduced, and then probabilistic diameter, probabilistic bounded, probabilistic semi-bounded, probabilistic unbounded and probabilistic totally bounded sets are introduced. Also, we prove that in every probabilistic metric, every probabilistic totally bounded set is probabilistic bounded set. We also present the cantor intersection theorem and a formulation of Bair’ s Theorem in complete probabilistic metric spaces. In addition, we prove that the Heine-Borel property and the Bolzano-Wierestrass property are equivalent.

Despite the fact that using the services of outsourced data stream servers has extremely been welcomed, but still the problem of obtaining certainty about received results from these servers is one of the basic challenges in enterprises. For outsourcing these services, the user should be assured by a mechanism about the security of communication channels as well as the correct and honest function of the server, because the server may attack the integrity of the results due to economic and malicious reasons. In such attacks, some parts of results are not sent to the user or sent after being modified or delayed. In this article, we have come up with an efficient method for detecting integrity attacks in outsourced data steam systems based on auditing the results of cross computation. In this method, the main data stream has been enciphered by a key and a small part of data has been enciphered by a different key, as a dependant data stream, and sent to the server. The requested query is applied on both streams and the user judges the integrity of results by comparing the results. Our method imposes a little overhead on the user and needs no change in the structure of the server. The probabilistic modeling of the method shows that this method has a high efficiency and the results of the exprimental analysis confirm this very well.

The aim of this paper is to study the Completeness of L-quasi-uniform convergence spaces and L-quasi-uniform spaces. Firstly, we describe L-quasi-uniform convergence spaces as enriched categories. Then we give two kinds of Completeness of L-quasi-uniform convergence spaces and show that Lawvere Completeness implies Cauchy Completeness. Finally, we use the Cauchy Completeness of L-quasi-uniform convergence spaces to define the Cauchy Completeness of L-quasi-uniform spaces, and show that Cauchy Completeness is equivalent to Lawvere Completeness in L-quasi-uniform spaces.

Background and Aim: A major quality assurance target is minimizing error rates to enhance patient safety. Clinical laboratories have long focused their attention on quality control methods and quality assessment programs. The current study aimed to investigate the Completeness of specimen labeling in the histopathology department. Materials and Methods: In this cross-sectional retrospective study, we analyzed labels of tissue samples sent from Orthopedics, Neurosurgery, Internal medicine, Urology, ENT, Surgery, ICU, and Endoscopy wards over three months in Urmia Imam Khomeini hospital from January 2023 to March 2023. All information including the patient's name, age, patient file number, tissue type, anatomical location, sampling date, name of the referring physician, legibility of written information, two patient identifiers (full name, date of birth or file number), and affixing the label on the body of the container was checked. Results: Of the 2178 pathology samples examined, the largest numbers of samples (53.58%) were sent from the surgery department and the least (0.69%) from the neurosurgery Ward. The lowest number of errors was related to the patient's age, which ranged from 0% in the internal medicine, neurosurgery and, endoscopy to 8.5% in the urology Ward. There was a statistically significant difference between the criteria obtained in different wards, except for the patient's name and illegibility of written information.   P-value was <0.001 for patient age, file number, tissue type, sampling date, doctor's name, label on container body and two-identifier registration, and 0.049 for the anatomical position of the sample. Conclusion: This study showed that there is a variety of errors in labeling pathology samples. This shows that the high volume of work and a large number of samples cannot be the reason for the error in the labeling. Due to the similarity of names, two samples may be mistaken for each other, but the presence of the second identifier solves this problem. Newer technologies such as bar coding may reduce the frequency of specimen labeling errors.

In Classical Logic, an argument is deemed valid if and only if it lacks a counterexample. However, arguments like  and  are considered valid based on this definition, despite natural intuition challenging their validity. A New Outlook on the Elements of Logic introduces a novel definition for argument validity, rendering the aforementioned arguments unprovable. This new definition necessitates revisions in argument evaluation, the substitution rule, the definition of logical truth, methods for determining argument validity and invalidity, as well as the definition and procedure of Soundness and Completeness proofs in Classical Logic. The establishment of the Truth-Functional System of Propositional Logic stems from this revised definition.Asadollah Fallahi critiques this system in "Hajhosseini’s Truth-Functional Semantics," published in Philosophy and Kalam, 2023, Vol. 56, issue 1. While proposing scattered criticisms, this article reveals that, aside from one critique requiring rectification due to an inadvertent mistake, the other criticisms stem from fallacies, unfounded accusations, non-compliance with certain critique conditions, incorrect formulation of the definition of a valid argument, and oversight of consequences arising from new conditions for argument validity and its definition.

Development of E-banking has modified the structure of banking business and banking performance, efficiency, risk and challenges which have also been articulately recognized based on the international best practices. E-banking brazenly expedites and streamlines financial transactions via enhancing technology and expanding the bank services in comparison with conventional banking. Accordingly, online access to the banks’ products, financial statements, payment services and even credit scoring has considerably improved bank-customer relationships in the context of lending and borrowing practice, deposit composition, investment opportunities, trade finance options as well as account management diversification. The impact of recent E-banking developments on banking is statistically tested for the banking network of Iran using Dynamic Panel Data approach. Results indicate that the ratio of ATMs and Electronic Cards to bank assets positively and significantly influence profitability ratios. Meanwhile, the ratio of online branches and Pin Pads to the banks' assets negatively and significantly affects profitability although the transaction volumes have surged for the banks under study.

This research aims to develop a domestic model to rank Iranian banks based on their function to evaluate Soundness and stability. For this purpose, after studying the related literature, a model with six dimensions and thirty factors is designed and validated using Delphi-Fuzzy method. This resulted in a model with six dimension and twenty six factors. Then, using network analysis and applying Dematel technique, the final model and the weights of each factor were determined. We used the model to evaluate the performance of the several banks in year 1393. And then they were ranked by using TOPSIS technique. The results show that Pasargad, Khavarmiyane, Karafarin, Dey and Sina banks had better function in comparison to other studied banks in 1393.

In Data Outsourcing, the owner surrenders his data management operations to an external provider which receives user queries and answers them. Besides, data may be of great importance to owners while the external provider may not be trustworthy. Thus, providing data privacy and integrity of user queries have to be considered. Here data privacy means that owner's data must not be revealed to service provider; and query integrity means that the result set returned to users must be sound, complete, and up-to-date. Different methods are proposed to handle mentioned goals with their own advantages and disadvantage, namely encryption usage, private information retrieval (PIR) and data distribution. In this article, we have proposed an approach to gain mentioned goals. Our approach provides better performance and it also provides data privacy and integrity of queries.