#### DMCA

## Resource-Bounded Reasoning about Knowledge (2001)

Citations: | 2 - 0 self |

### BibTeX

@MISC{Ho01resource-boundedreasoning,

author = {Ngoc Duc Ho and Von Fakultat and Mathematik Informatik and Univertit'e De Caen},

title = {Resource-Bounded Reasoning about Knowledge},

year = {2001}

}

### OpenURL

### Abstract

The main goal of the thesis is to develop a framework for modeling resource-bounded reasoning of realistic agents and to provide formal theories of rational agency with a solid epistemic foundation. The concept "agent" has turned out to be a very useful abstraction for conceptualization in different areas of Computer science. In most agent theories, agents are treated as intensional systems which are characterized by means of mentalistic concepts like knowledge, beliefs, goals, and intentions. Among them, the epistemic concepts (knowledge and belief) are among the most important ones and have been studied most intensively. They are usually formalized using systems of modal logic. However, the modal approach to epistemic logic has a major drawback: it suffers from the so-called logical omniscience problem (LOP). It requires agents to know all logical truths and all logical consequences of their knowledge. So the modal approach to epistemic logic is not suited to formalize resource-bounded reasoning, and the issue of resource-boundedness remains one of the main foundational problems of any agent theory that is developed on the basis of modal epistemic logic. To solve the LOP I propose a strategy of modeling knowledge that takes the cost of reasoning seriously. The main intuition is that an agent may not know the consequences of his knowledge if he does not perform the necessary reasoning actions. Because reasoning requires resources, it cannot be safely assumed that the agent can compute his (implicit) knowledge if he does not have enough resources to perform the required reasoning. In modal epistemic logic, the usual form of an epistemic axiom is: "if an agent knows all premises of a valid inference rule then he also knows the conclusion". In contrast, I have argued that the correct form of epistemic axioms should be: "if an agent knows all premises of a valid inference rule and if he performs the right reasoning, then he will know the conclusion as well". This idea is captured formally using a variant of dynamic logic: the result is a family of dynamic-epistemic logics that formalizes the concept of explicit knowledge, which solve all variants of the logical omniscience problem and at the same time account for the intuition that agents are rational. Explicit knowledge can - in contrast to implicit knowledge - provide justification for actions. However, explicit knowledge alone is not enough for modeling agency. First, there are too few statements about explicit knowledge that can claim validity. Second, it is not the only kind of knowledge that agents can act upon. Certain actions not only depend on what agents currently know but also on what they can compute within specific amounts of time. If an agent needs to make a decision within 1 hour then anything that he can compute within that time is relevant for his decision. Thus, in order to predict and to explain an agent's action correctly we need a framework for describing what an agent can know under some specified resource constraints. For that purpose I have introduced a concept of knowledge which contains a direct reference to the amount of available resources. It can be described informally as follows. An agent knows p within n time units if he can compute p _reliably_ within n units of time. That is, if he chooses to compute p then he will succeed after at most n time units. The qualification "reliable" makes the agent's action predictable: agents can act upon knowledge that can be computed reliably. For formalizing this concept of knowledge, I have provided a framework that combines epistemic logic with complexity analysis. I have shown that within that framework, resource-bounded reasoning can be formalized correctly, the relationship between knowledge, reasoning, and the availability of resources can be established, the problems of traditional approaches can be avoided, and rich epistemic logics can be developed which can account adequately for our intuitions about knowledge.

### Keyphrases

explicit knowledge resource-bounded reasoning agent theory modal approach valid inference rule time unit epistemic axiom modal epistemic logic specific amount different area formal theory so-called logical omniscience problem correct form main foundational problem time account solid epistemic foundation important one certain action major drawback concept agent computer science epistemic concept resource constraint intensional system modal logic right reasoning logical omniscience problem enough resource main intuition dynamic logic logical consequence useful abstraction available resource usual form necessary reasoning action rich epistemic logic qualification reliable direct reference dynamic-epistemic logic rational agency epistemic logic complexity analysis main goal logical truth mentalistic concept realistic agent traditional approach required reasoning