Research On Some Problems About The Knowledge Representation And Reason

Knowledge representation and reasoning (KRR) are indispensable to the effective computer processing of knowledge and information. KRR is the main research area in symbolic artificial intelligence (AI). In the field of KRR, logic plays an important role. The study of KRR mainly includes the following: the formalization of all kinds of knowledge types by means of logic, the construction of an axiom system and the investigation of the system's semantics and computational complexity. KRR has been widely studied from 1980's. Several reasoning systems such as fuzzy reasoning, uncertain reasoning, non-monotonic reasoning, paraconsistent logic and so on, have been proposed to achieve effective reasoning for processing knowledge and information in artificial intelligence. All the above studies motivated by solving the challenges in artificial intelligence not only have made use of the results of mathematical logic, but also have extended the scope of classical logic and thus have become an important part of modern non-classical logic studies.This paper focuses on the following issues related to KRR:(I) Studies on Non-sufficient Reasoning In classical logic, the fact thatΓ?αis true meansΓis the sufficient condition ofα. In other words, ifΓis true, then so isα. In artificial intelligence and practical applications, the available information is usually incomplete. In this situation, the blind pursuit of the logical consequence in the sense of classical logic is impractical. We are more interested in the reasoning methods with"reasonableness". This paper will discuss the study on non-sufficient reasoning.In the framework of finite proposition language, we define the background of the non-sufficient reasoning---epistemic structure. It is defined as the set of all the facts which the agent can judge true or false in a finite language. Inspired by the notion of basal in linear space, we introduce the basal of epistemic structure ---epistemic basal and prove that the epistemic structure can be completely determined by its epistemic basal. An epistemic system comprises epistemic structures and a partial order which can reflect the strength of the epistemic ability of the epistemic structure. On the basis of epistemic system, we propose three syntax rules of non-sufficient reasoning and its categories lattice semantic and establish the corresponding representation theorem.In order to generalize the above work, we introduce the notion of infinite epistemic structures and the limit of a sequence of infinite epistemic structures. We further prove the existence of the limit of some sequences of infinite epistemic structures. Based on the three syntax rules of non-sufficient reasoning in finite language, we add a limit reasoning rule to describe the non-sufficient reasoning relations under infinite language. Finally, we construct the categories lattice semantic model of infinite epistemic structure and show the corresponding representation theorem. (II) Studies on Iterated Belief Revision in Absent ValuationThe knowledge or belief of the Agent is not unchangeable, but changes with the change of external environment or its own state. The ideal epistemic state of Agent is a state of equilibrium. When new knowledge is acquired, this state of equilibrium will be broken, and the Agent shall adjust its belief state to reach a new equilibrium. This adjustment process is exactly the process of belief revision.Classical AGM belief revision theories and iterated belief revision theories represented by D-P System are both developed in the framework of complete valuations. Due to the limitations of technology and learning tools, our understanding of the world during a particular period could also be partial and limited. In this case, it is more appropriate to use absent valuation, i.e. assigning one of the three possible values (true, false, or unknown) to an atomic proposition, to study problems.We extend the D-P System to absent valuation. Different from complete valuation, absent valuation may assign the unknown state to some atomic propositions. Adopting absent valuation as possible world, we define the especial relation between absent valuations---the supplementary valuation. Finally, we establish a model-based representation theorem which characterizes the proposed postulates and constraints.(III) Studies on Similarity and Equivalence of Epistemic States It is generally recognized that non-monotonic reasoning and belief revision is just like the two sides of a coin and that there exists a fundamental relation between the two. The concept of epistemic states (i.e., ES) introduced by Bochman aims to provide the two with a unified semantic framework.In logic system research, using the structural properties of semantic structure to describe the necessary and sufficient condition of equivalence among semantic structures is an important and fundamental research area. Bochman proposed the concept of similarity in ES, and introduced skeptical equivalence—a concept to describe the semantic equivalence among ES based on the consistency of external reasoning behavior of ES. Unfortunately, he did not further study the internal relations of the two. This paper will conduct study on this point. It can be shown that two similar ES must also be skeptically equivalent while the inverse proposition is not true, i.e., skeptically equivalent ES may not necessarily be similar. In order to explore the relationship between similarity and the reasoning behaviors of epistemic states, a new notation called quasi-skeptical equivalence and an operator par(.) over epistemic states are introduced. We conclude that any pair of pure finite epistemic states are quasi-skeptically equivalent if and only if par( M 1) is similar to par( M 2), where par (.) is an operator working on ES.