Predicate Formulas Research Articles

A novel formal logic for formal analysis of timeliness in non-repudiation protocols

Non-repudiation protocols are aimed at exchanging digital messages and irrefutable receipts between two mistrusting parties over the Internet, which form the cornerstones of modern secure network transactions. Timeliness is a key security property of non-repudiation protocols, which ensures that protocol agents can terminate their execution within a finite time, and guarantees the satisfaction of time-constraint among protocol events. A number of analysis methods have been proposed, but most of them cannot explicitly express the time factor which plays an important role in protocols. In order to address the challenge of analyzing timeliness, this paper extends the logic of events theory (LoET) and proposes a novel formal logic. By explicitly introducing the time factor into predicate formulas, the new logic can model actions, knowledge, and process states of each agent at different time points, thus enhancing its ability of time description. The formal semantics of new logic is given to avoid ambiguity of logic language and guarantee the soundness of new logic. A typical non-repudiation protocol is analyzed with new logic, and the timeliness flaw is discovered. The proposed logic overcomes the limitations of LoET in terms of time description and effectively addresses the issue of the inability to analyze timeliness.

A Generalized Realizability and Intuitionistic Logic

Let V be a set of number-theoretical functions. We define a notion of V -realizability for predicate formulas in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this article, we prove that Intuitionistic Predicate Calculus is sound with respect to the semantics of V -realizability if and only if some natural conditions for V hold.

Philosophy is reflective…or not?

The article focuses on the historical background for a logic-and-meaning approach to consciousness as tselostnost’. This notion, having no equivalent in English, may roughly be rendered as "a (self)developing whole". The author demonstrates that in the thought experiment "soaring man" Ibn Sina discovers the pure self as an unavoidable condition of our consciousness. This self is revealed to itself in a different way, in a different cognitive act than any object of knowledge. Then Descartes’ discovery of the ‘S is P’ predication formula as a condition for multiplicity of our phenomenal ego is discussed. The line can be traced back to Nicolas of Cusa, who discovered development and envelopment, and continued to a contemporary French sinologist Francois Jullien, who argues that, paradoxically, the ultimate foundations of any philosophical tradition cannot be clarified and reflected upon by means of that very tradition.

Rule Fusion of Privacy Protection Strategies for Co-Ownership Data Sharing

With the rapid development of social networks, personal privacy leakage has become more and more serious. A social network is a shared platform. Resources in a social network may be shared by multiple owners. In order to prevent privacy leakage, each owner assigns a corresponding privacy protection strategy. For the same shared contents, integrating the privacy protection strategies of all owners is the key problem for sharing. This paper proposes a rule fusion method of privacy protection for the co-ownership of data shared in social networks. First, the content of the protection is defined according to different privacy requirements. Second, this paper uses predicate logic formulas to abstract the natural language-based description of privacy protection and further provides a logical model of privacy protection rules. Third, this paper gives the definition of privacy protection heterogeneous rules and provides a rule fusion algorithm to ensure no conflict exists among these rules. The experimental results show that the proposed rule-based fusion method of privacy protection strategy performs at a higher level than the privacy protection strategy fusion.

Extraction of common properties of objects for creation of a logic ontology

The paper describes an approach to the formation of ontology based on descriptions of objects in terms of the predicate calculus language. With this approach, an object is represented as a set of its elements, on which a set of predicates is defined that defines the properties of these elements and the relationship between them. A description of an object is a conjunction of literals that are true on elements of an object. In the present work, ontology is understood as an oriented graph with descriptions of subsets as nodes and such that the elements of a set at the end of an oriented edge have the properties of the elements of the set at the beginning of this edge. Three settings of an ontology construction problem are considered: 1) all predicates are binary and subsets of the original set of objects are given; 2) all predicates are binary and it is required to find subsets of the original set; 3) among the predicates there are many-valued ones and subsets of the original set of objects are given. The main tool for construction such a description is to extract an elementary conjunction of literals of predicate formulas that is isomorphic to subformulas of some formulas. The definition of an isomorphism of elementary conjunctions of atomic predicate formulas is given. The method of ontology construction is formulated. An illustrative example is provided.

Generalized Realizability and Basic Logic

Let V be a set of number-theoretical functions. We define a notion of absolute V -realizability for predicate formulas and sequents in such a way that the indices of functions in V are used for interpreting the implication and the universal quantifier. In this article, we prove that Basic Predicate Calculus is sound with respect to the semantics of absolute V -realizability if V satisfies some natural conditions.

Сравнение различных представлений знаний для сложных структурированных объектов при решении задач ИИ

The problem of knowledge representation for a complex structured object is one of the actual problems of AI. This is due to the fact that many of the objects under study are not a single indivisible object characterized by its properties, but complex structures whose elements have some known properties and are in some, often multiplace, relations with each other. An approach to the representation of such knowledge based on first-order logic (predicate calculus formulas) is compared in this paper with two currently widespread approaches based on the representation of data information with the use of finite-valued strings or graphs. It is shown that the use of predicate calculus formulas for description of a complex structured object, despite the NP-difficulty of the solved problems arising after formalization, actually have no greater computational complexity than the other two approaches, what is usually not mentioned by their supporters. An algorithm for constructing an ontology is proposed that does not depend on the methodof desc ribing an object, and is based on the selection of the maximum common property of objects from a given set.

Generalized Realizability and Markov’s Principle

Various variants of the concept of the V-realizability for predicate formulas are defined where indices of functions in the set V are used for interpreting the implication and the universal quantifier. It is proved that Markov’s principle is weakly V-realizable, not uniformly V-realizable, and uniformly V-realizable in any V-enumerable domain M ⊆ ℕ.

Polynomial Equivalence of the Problems “Predicate Formulas Isomorphism and Graph Isomorphism”

The problem of isomorphism checking of two elementary conjunctions of predicate formulas is considered in this work. Such a problem appears while solving some Artificial Intelligence problems, admitting formalization by means of predicate calculus language. The exact definition of the concept of isomorphism of such formulas is given in this paper. However, isomorphic elementary conjunctions of predicate formulas are formulas that, with some substitution of variables instead of their arguments, coincide with the accuracy of the order of writing literals. Problems are described that, when solved, mean the necessity of testing formulas for isomorphism arises. Polynomial equivalence of this problem with the Graph Isomorphism (GI) problem is proved.

Absolute L-Realizability and Intuitionistic Logic

An absolute L-realizability of predicate formulas is introduced for all countable extensions L of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.

Proposition and Predication

Subject-predicate linkage and its role in language and metaphysics is the point where the immanent logic of thought and its relation to reality uncover themselves. The logic of predication displays itself in language in the elementary proposition. For Indo-European languages, the core predication formula is “S is P.” It is backed by a universal intuition of a closed space, as exemplified by Euler diagram. The formal logic based on that type of the subject-predicate linkage may be called substance-based logic. The “S is P” construction is not possible in natural Arabic. This language uses an alternative predication formula for connecting subject to predicate, which in the terminology of traditional Arabic grammar is designated as “S isnād P” where isnād literally means “leaning.” This Arabic elementary proposition reflects the basic intuition of the flux, the intuition of continuous process of flowing. The logic based on of this type of subject-predicate linkage is referred to as process-based logic.

Method of accurate-fast magnitude estimation for earthquake early warning -----Trial and application for the 2008 Wenchuan earthquake

Earthquake early warning (EEW) system is one of the most useful tools to mitigate seismic hazards. Although EEW approaches have already been developed worldwide, the issues of improving the accuracy and applicability were still controversial. On the basis of the existing measurable parameters related to the earthquake magnitude, we proposed a method in terms of the squared integral displacement (ID2) to anticipate the magnitude in real-time for EEW purpose that can be used for large earthquakes. With the main-shock and aftershocks of the 2008 Ms 8.0 Wenchuan earthquake, we investigated the regression relationships between the proposed ID2 and earthquake magnitude, based on which the magnitude predication formula was derived. Then the predicated accuracy from ID2 was compared with that from τc and Pd. By comparing the differences between the estimated and reported magnitudes, the proposed ID2 method was of the highest accuracy among the investigated 3 parameters. Next we analysed the ground motion characteristics in the frequency domain and established the correlations between the Fourier amplitude and spectral intensity of the initial P wave with the magnitude estimation differences, based on which a revision method of reducing such differences was put forward and the saturation effects of predicting large magnitudes were well mitigated simultaneously.

Автоматизация процедуры идентификации объектов на основе логики предикатов

One of the defining tasks in automating the processing of current information obtained in the process of object research is the possibility of assigning it to specific objects located in the database (DB) of the information system. Such a task can be represented as a task of identifying the objects of analysis (monitoring) on current data. Initial information about a particular facility during the research can come from different sources and be incomplete and inaccurate. Due to identification, received data for each object are accumulated in the database for further automated analysis. But in a number of cases, the current information contains not specific names of the research objects of interest, but only some signs of their functioning: location, operating time, numerical characteristics of objects, etc. In such conditions, the identification of objects can occur on the basis of similarity of semantic features contained in the current information and attributes which have been already accumulated by the objects of research in the database. A distinctive feature of the subject area in which the analysis of objects is made is its variability; therefore, with the passage of time, the attributes serving to identify the objects may change. The addition of new features will result in a change in application software and will require the involvement of developers, which leads to additional time costs and decrease in the speed of procedure for identifying objects. This reason leads to the need to create a new approach to the automation of object monitoring, based on such requirements as high quality of the decisions made and ability to quickly change the logic of identification in the process of the system. The paper proposes the possibility of using predicate logic formulas, with the aim of making new information in the database more quickly and assigning it to a specific object, which makes it possible to develop the fastest solution.

Extraction of a maximal common sub-formula of predicate formulas for the solving of some Artificial Intelligence problems

Extraction of a maximal common sub-formula of predicate formulas for the solving of some Artificial Intelligence problems

Arithmetical realizability and basic logic

Absolute arithmetical realizability of predicate formulas is introduced. It is proved that the intuitionistic logic is not correct with this semantics, but the basic logic is correct.

On similarity in fuzzy description logics

This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics. For this purpose we use concrete domains in the fuzzy description logic IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these objects.

Self-training Network with the Sells Implementing Predicate Formulas

A model of self-modificated predicate network with cells implementing predicate formulas in the form of elementary conjunction is suggested. Unlike a classical neuron network the proposed model has two blocks: a training block and a recognition block. If a recognition block has a mistake then the control is transfered to a training block. Always after a training block implementation the configuration of a recognition block is changed. The base of the proposed logic-predicate network is a logic-objective approach to AI problems solving and level description of classes as well as the notion of partial deducibility which allows to extract common sub-formulas of elementary conjunctions

Fuzzy inequational logic

We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes their semantic entailment and provability in graded setting which allows to draw partially true conclusions from partially true assumptions. We follow the Pavelka approach and define general degrees of semantic entailment and provability using complete residuated lattices as structures of truth degrees. We prove the logic is Pavelka-style complete. Furthermore, we present a logic for reasoning about graded if–then rules which is obtained as particular case of the general result. • A truth-functional logic for reasoning with graded inequalities is proposed. • Its semantics is defined using algebras with fuzzy orders. • Completeness in the Pavelka style is established for all complete residuated lattices. • A complete abstract logic of graded attributes is shown as an application.

Secure Outsourced Attribute-Based Signatures

Attribute-based signature (ABS) enables users to sign messages over attributes without revealing any information other than the fact that they have attested to the messages. However, heavy computational cost is required during signing in existing work of ABS, which grows linearly with the size of the predicate formula. As a result, this presents a significant challenge for resource-constrained devices (such as mobile devices or RFID tags) to perform such heavy computations independently. Aiming at tackling the challenge above, we first propose and formalize a new paradigm called Outsourced ABS, i.e., OABS, in which the computational overhead at user side is greatly reduced through outsourcing intensive computations to an untrusted signing-cloud service provider (S-CSP). Furthermore, we apply this novel paradigm to existing ABS schemes to reduce the complexity. As a result, we present two concrete OABS schemes: i) in the first OABS scheme, the number of exponentiations involving in signing is reduced from $O(d)$ to $O(1)$ (nearly three), where $d$ is the upper bound of threshold value defined in the predicate; ii) our second scheme is built on Herranz et al.’s construction with constant-size signatures. The number of exponentiations in signing is reduced from $O(d^2)$ to $O(d)$ and the communication overhead is $O(1)$ . Security analysis demonstrates that both OABS schemes are secure in terms of the unforgeability and attribute-signer privacy definitions specified in the proposed security model. Finally, to allow for high efficiency and flexibility, we discuss extensions of OABS and show how to achieve accountability as well.

Extended Fuzzy Constructive Logic

A logical system is introduced that is similar to the “fuzzy constructive logic” earlier developed by the author, but gives wider possibilities of establishing the truth of predicate formulas and logical deductions in the framework of this logic. The notions of strong and weak FCL∗ -validity of predicate formulas are defined. It is proved that every formula deducible in the constructive (intuitionistic) predicate calculus is strongly FCL∗ -valid. On the other hand, it is proved that some formulas not deducible in this calculus are not weakly FCL∗ -valid. A definition is given for the semantics of the traditional constructive logic on the base of the developed logical apparatus. Theorems are proved showing differences between the extended fuzzy constructive logic and the traditional constructive logic. Bibliography: 38 titles.