Don Faust教授两场学术报告
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1. 主题：The Perspective of EXPLORATIONISM and The Structure of Evidential Gluts and Gaps
时间：9月16日（周二）上午9:00－11:30 地点：中国人民大学人文楼6层会议室
2. 主题：Knowledge Representation Issues
时间：9月18日（周四）晚上18:00－20:30 地点：中国人民大学明德主楼0204教室

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讲座概要

1. The Perspective of EXPLORATIONISM and The Structure of Evidential Gluts and Gaps

If our knowledge is absolute and consistent, then we can use Classical Logic.If it is not absolute but remains consistent, then it is often the case that our knowledge is evidential in nature, indeed regularly involving evidential gluts and evidential gaps as well, and Evidence Logic (EL) provides an example of a suitable foundational framework.Of course, if the conflict we are dealing with rises to the level of contradiction, then EL is also inadequate and one must use a paraconsistent logic.

So EL provides a framework for this middle ground where evidential conflict commonly occurs yet no contradictions arise.EL also provides logical machinery helpful in studying further the concept of negation, which is certainly of foundational importance to paraconsistency.In EL, for a predication P, Pc:e asserts that there is confirmatory evidence at the value e for P while Pr:e asserts refutatory evidence at value e.See “The Concept of Evidence”, INT. J. INTELL. SYSTEMS 15 (2000), 477-493 for precise definitions and theorems delineating EL and its Boolean Sentence Algebras, and “Conflict without Contradiction: paraconsistency and axiomatizable conflict toleration hierarchies in Evidence Logic”, LOGIC AND LOGICAL PHILOSOPHY 9 (2001), 137-151 for initial examples of families of extensions of EL whose axioms reach out in a variety of ways toward domain-specific properties regarding evidential conflict.

In this talk we will initially look, mostly rather informally, at how evidential gluts and gaps are each structured in EL and also how they interact.Subsequently we will formally examine three families of axiomatized extensions of EL:a previously introduced family of logics each allowing no conflict at some evidence value e, a new family each allowing no paucity at value e, and a new “conjunctive” family each both allowing no conflict at value e1and allowing no paucity at value e2.Further, continuing formally and motivated by the evidential contexts most common in EL application domains, we will generalize the notions of conflict and paucity and examine the resulting theories.The Boolean Sentence Algebras are analyzed in each case.

Throughout we keep in mind, and indeed interpret into EL, Aristotle’s work on privatives which even 2000 years ago helped to further elucidation of the concept of negation.His opinion that non-P IMPLIES (NOT P) is closely related to the evidential gluts we define and study in EL, while the converse of this opinion connects with our evidential gaps in EL.By looking at some of the EL-theories as described above, which in fact model a gradational version of the concept of privation, analysis of the interplay between privation and classical negation is achieved, and further insight into the general concept of negation is hopefully gained.

2. Knowledge Representation Issues

Knowledge representation issues form an integral part of many careful attempts to explore principal problem areas of epistemology.Here we will consider three such issues, having to do with (1) the concept of negation, (2) the notion of belief, and (3) the notion of visual knowledge.

The concept of negation was carefully considered by both Aristotle and Indian philosophers.We will visit their considerations, and then use their insights to expand the explicatum of negation from that which occurs in Classical Logic to that which occurs in Evidence Logic.

Belief systems, we will argue, are all unnecessary.By definition, we will say that agent A believes a sentence S if A asserts S is true although A does not know (have absolute evidence) that S is true.We will argue that in all contexts where one might view beliefs as necessary, they are replaceable by a type of ‘minimal assertion’ which will be called commitment, and which involves no belief in the sense we have defined it.

Regarding the notion of visual knowledge, we are all familiar with the old saying, “a picture is worth a thousand words”.In this talk we will discuss preliminary explorations which, roughly put, try to answer the question:

“Yes, … but if so, then

what is that thousand words that a picture is worth?”

We will set up a logic with a pixel-based semantics (model theory), attempting to build (a logical realization of) a picture as the limit of increasingly rich approximations to it, and hence (a logical realization of) “the thousand words the picture is worth” as “the limit of the theories of these approximations”.

This talk should involve lively discussion, and I hope your input will help both you and me to learn more about what I am trying to do here in this attempt to more crisply elucidate the concept of visual knowledge.

中国人民大学现代逻辑与科学技术哲学研究所
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