Formal Logic Language Research Articles

A Comparative Study on Modality: Relevance Theory versus Possible World Theory in Semantics

Language users use symbolic language expressions to communicate, and the meaning of sentences delivered is analyzed through correspondence with entities that exist in the real world. However, speakers do not always try to communicate based on the one world they belong to, and through a grammatical system called modality, they can communicate not only about the real world but also about the various possible worlds that exist. This means that statements about situations other than facts, i.e., hypothetical situations or states, can be expressed using modality, and the meaning of sentences can be analyzed through a concept of semantics as a possible world, and also through relevance theory in pragmatics. This study investigates the meaning of modal verbs through each of the two theories. First, the meaning of modal verbs is divided into necessity and possibility through existing research on modality. This analysis follows a definition of the core meaning of each modal verb through relevance theory, and evokes derivative meanings according to the context of occurrence. Possible world semantics, on the other hand, logically explains the various meanings of modal verbs by generating the real world and countless possible worlds through close connectivity using formal logical language of semantic representations from a polysemous perspective.

Research on RFID authentication Protocol in Internet of Vehicles

With the development of Internet of Vehicles, radio frequency identification technology (RFID) has been widely used in vehicle networks. The classic RFID authentication scheme cannot meet the special security and confidentiality requirements of RFID in Internet of Vehicles. This paper proposes an RFID authentication protocol in the Internet of Vehicles based on the certification center (CA). Through the certification center, you can avoid the Dos attack problem faced by the back-end server and reduce the server's computing burden. At the same time, through the authentication center, the identity authentication of the back-end server, reader and vehicle tag is indirectly achieved, which solves the problems of replay and malicious tracking that are often faced in RFID. The theory of formal logic language GNY proves that the protocol has high security in the Internet of Vehicles.

Conditional probability logic, lifted Bayesian networks, and almost sure quantifier elimination

We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively speaking, although formal details are different, CPL can express the same kind of statements as some languages which have been considered in the artificial intelligence community. We also consider a way of making precise the notion of lifted Bayesian network, where this notion is a type of (lifted) probabilistic graphical model used in machine learning, data mining and artificial intelligence. A lifted Bayesian network (in the sense defined here) determines, in a natural way, a probability distribution on the set of all structures (in the sense of first-order logic) with a common finite domain D. Our main result (Theorem 3.14) is that for every “noncritical” CPL-formula φ(x¯) there is a quantifier-free formula φ⁎(x¯) which is “almost surely” equivalent to φ(x¯) as the cardinality of D tends towards infinity. This is relevant for the problem of making probabilistic inferences on large domains D, because (a) the problem of evaluating, by “brute force”, the probability of φ(x¯) being true for some sequence d¯ of elements from D has, in general, (highly) exponential time complexity in the cardinality of D, and (b) the corresponding probability for the quantifier-free φ⁎(x¯) depends only on the lifted Bayesian network and not on D. Some conclusions regarding the computational complexity of finding φ⁎ are given in Remark 3.17. The main result has two corollaries, one of which is a convergence law (and zero-one law) for noncritial CPL-formulas.

Formal logical language to set requirements for secure code execution

Presently, a special attention is paid to the problem of information security when designing and using objects of critical information infrastructure. One of the most common approaches used to secure the information processed on these objects is the creation of an isolated program environment (sandbox). The security of the environment is determined by its invariability. However, the evolutionary development of data processing systems makes it necessary to implement new components and software in this environment on the condition that the security requirements are met. In this case, the most important requirement is trust in a new program code. This paper is devoted to developing a formal logical language to describe functional requirements for program code that allows one to impose further constraints at the stage of static analysis, as well as to control their fulfillment in dynamics.

Логика первого порядка для задания требований к безопасному программному коду

Currently the problem of information security during designing and exploiting the objects of critical information infrastructure is paid special attention to. One of the most common approaches to providing information security, processed on the objects, is creating isolated programming environment. The environment security is determined by its invariability. However, the evolutional development of data processing systems gives rise to the necessity of implementing the new components and software in this environment under condition that security requirements are satisfied. The most important requirement consists in trust in the new programming code. The given paper is devoted to developing formal logical language of description of functional requirements for programming code, allowing to make further demands at the stage of static analysis and to control their implementation in dynamics.

An institution theory of formal meta-modelling in graphically extended BNF

Meta-modelling plays an important role in model driven software development. In this paper, a graphic extension of BNF (GEBNF) is proposed to define the abstract syntax of graphic modelling languages. From a GEBNF syntax definition, a formal predicate logic language can be induced so that meta-modelling can be performed formally by specifying a predicate on the domain of syntactically valid models. In this paper, we investigate the theoretical foundation of this meta-modelling approach. We formally define the semantics of GEBNF and its induced predicate logic languages, then apply Goguen and Burstall's institution theory to prove that they form a sound and valid formal specification language for meta-modelling.

A Comprehensive Introduction to Lacan's Theories of Psychosis

A Comprehensive Introduction to Lacan's Theories of Psychosis

On the role of language in social choice theory

Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn into definability results of formal logic. The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible.

Quantifier probability logic and the confirmation paradox

Exhumation and study of the 1945 paradox of confirmation brings out the defect of its formulation. In the context of quantifier conditional-probability logic it is shown that a repair can be accomplished if the truth-functional conditional used in the statement of the paradox is replaced with a connective that is appropriate to the probabilistic context. Description of the quantifier probability logic involved in the resolution of the paradox is presented in stages. Careful distinction is maintained between a formal logic language and its semantics, as the same language may be outfitted with different semantics. An acquaintance with sections 1–5 of Hailperin (2006) covering the sentential aspects of probability logic is assumed as background information for quantifier probability logic.

Bringing ontology to the Gene Ontology

We present an analysis of some considerations involved in expressing the Gene Ontology (GO) as a machine-processible ontology, reflecting principles of formal ontology. GO is a controlled vocabulary that is intended to facilitate communication between biologists by standardizing usage of terms in database annotations. Making such controlled vocabularies maximally useful in support of bioinformatics applications requires explicating in machine-processible form the implicit background information that enables human users to interpret the meaning of the vocabulary terms. In the case of GO, this process would involve rendering the meanings of GO into a formal (logical) language with the help of domain experts, and adding additional information required to support the chosen formalization. A controlled vocabulary augmented in these ways is commonly called an ontology. In this paper, we make a modest exploration to determine the ontological requirements for this extended version of GO. Using the terms within the three GO hierarchies (molecular function, biological process and cellular component), we investigate the facility with which GO concepts can be ontologized, using available tools from the philosophical and ontological engineering literature.

Ddl Unlimited: Dynamic Doxastic Logic for Introspective Agents

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical language: a dynamic modal logic.1 Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL).2 This framework may be seen as an extension of standard Hintikka-style doxastic logic (Hintikka 1962) with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about

Formal Logic and Ordinary Language

Formal Logic and Ordinary Language

Formal Logic and Ordinary Language

Formal Logic and Ordinary Language