We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the model-checking problem.

Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higher-level belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness," where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning," where an agent is viewed as a "society of minds," each with its own cluster of beliefs, which may contradict each other.

We introduce a new approach to dealing with the well-known logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1

Proof-carrying code (PCC) is a framework for mechanically verifying the safety of machine language programs. A program that is successfully verified by a PCC system is guaranteed to be safe to execute, but this safety guarantee is contingent upon the correctness of various trusted components. For instance, in traditional PCC systems the trusted computing base includes a large set of low-level typing rules. Foundational PCC systems seek to minimize the size of the trusted computing base. In particular, they eliminate the need to trust complex, low-level type systems by providing machine-checkable proofs of type soundness for real machine languages. In this thesis, I demonstrate the use of logical relations for proving the soundness of type systems for mutable state. Specifically, I focus on type systems that ensure the safe allocation, update, and reuse of memory. For each type in the language, I define logical relations that explain the meaning of the type in terms of the oper-ational semantics of the language. Using this model of types, I prove each typing rule as a lemma. The major contribution is a model of System F with general references — that is, mutable cells that can hold values of any closed type including other references, functions, recursive types, and impredicative quantified types. The model is based on ideas from both possible worlds and the indexed model of Appel and McAllester. I show how the model of mutable references is encoded in higher-order logic. I also show how to construct an indexed possible-worlds model for a von Neumann machine. The latter is used in the Princeton Foundational PCC system to prove type safety for a full-fledged low-level typed assembly language. Finally, I present a semantic model for a region calculus that supports type-invariant references as well as memory reuse. iii

: The standard model of knowledge in multi-agent systems suffers from what has been called the logical omniscience problem: agents know all tautologies, and know all the logical consequences of their knowledge. For many types of analysis, this turns out not to be a problem. Knowledge is viewed as being ascribed by the system designer to the agents; agents are not assumed to compute their knowledge in any way, nor is it assumed that they can necessarily answer questions based on their knowledge. Nevertheless, in many applications that we are interested in, agents need to act on their knowledge. In such applications, an externally ascribed notion of knowledge is insufficient: clearly an agent can base his actions only on what he explicitly knows. Furthermore, an agent that has to act on his knowledge has to be able to compute this knowledge; we do need to take into account the algorithms available to the agent, as well as the "effort" required to compute knowledge. In this paper, we show...

Amal J. Ahmed Andrew W. Appel # Roberto Virga Princeton University {amal,appel,rvirga}@cs.princeton.edu Abstract We demonstrate a semantic model of general references --- that is, mutable memory cells that may contain values of any (statically-checked) closed type, including other references. Our model is in terms of execution sequences on a von Neumann machine

In their attempt to model and reason about the beliefs of agents, artificial intelligence (AI) researchers have borrowed from two different philosophical tradi-tions regarding the folk psychology of belief. In one tradition, belief is a relation between an agent and a proposition, that is, a propositional attitude. Formal analyses of propositional attitudes are often given in terms of a possible-worlds semantics. In the other tradition, belief is a relation between an agent and a sen-tence that expresses a proposition (the sentential approach). The arguments for and against these approaches are complicated, confusing, and often obscure and unintelligible (at least to this author). Nevertheless strong supporters exist for both sides, not only in the philosophical arena (where one would expect it), but also in AI. In the latter field, some proponents of posslble-worlds analysis have attempted to remedy what appears to be its biggest drawback, namely the assumption that an agent believes all the logical consequences of his or her beliefs. Drawing on initial work by Levesque, Fagin and Halpern define a logic of 9eneral awareness that superimposes elements of the sentential approach on a possible-worlds framework. The result, they claim, is an appropriate model for resource-limited believers. We argue that this is a bad idea: it ends up being equivalent to a more com-plicated version of the sentential approach. In concluding we cannot refrain from adding to the debate about the utility of possible-worlds analyses of belief.

In many domains agents must be able to generate plans even when faced with incomplete knowledge of their environment. We provide a model to capture the evolution of the agent's knowledge as it engages in the activities of planning (where the agent must attempt to infer the effects of hypothesized actions) and execution (where the agent must update its knowledge to reflect the actual effects of actions). The effects (on the agent's knowledge) of a planned sequence of actions are very different from the effects of an executed sequence of actions, and one of the aims of this work is to clarify this distinction. The work is also aimed at providing a model that is not only rigorous but can also be of use in developing planning systems.

this paper, I will discuss two aspects of SNePS propositional semantic networks [5, 8, 12, 17] that distinguish them as formalisms for the representation of knowledge---cables and paths. I will also discuss a kind of inference sanctioned by each one---reduction inference and path-based inference, respectively, and the integration of these two kinds of inference into a kind of "subconscious" reasoning. Informally, a semantic network is a labelled directed acyclic graph in which nodes represent entities and labelled arcs represent binary relations between entities. A propositional semantic network is a semantic network in which every proposition represented in the network is represented by a node, rather than by an arc. We will refer to a node that represents a proposition as a propositional node. Isolated nodes are not allowed in a semantic network, and since a semantic network is a variety of relational graph, it does not make sense to have two arcs with the same label emanate from the same node and terminate at the same node. However, there is no restriction forbidding several arcs with the same label from emanating from the same node if they terminate in different nodes. Informally, we will call a set of such arcs a cable. (We will formalize this below.) A propositional node, therefore, may have a set of cables emanating from it. Each cable represents an argument position of the proposition represented by the propositional node, the label

: In this survey, I attempt to identify and describe some of the common threads that tie together work in reasoning about knowledge in such diverse fields as philosophy, economics, linguistics, artificial intelligence, and theoretical computer science, with particular emphasis on work of the past five years, particularly in computer science. This articule is essentially the same as one that appears in Handbook of of Logic in Artificial Intelligence and Logic Programming, Vol. 4, D. Gabbay, C. J. Hogger, and J. A. Robinson, eds., Oxford University Press, 1995, pp. 1--34. It is a revised and updated version of a paper entitled "Reasoning about knowledge: a survey circa 1991", which appears in the Encyclopedia of Computer Science and Technology, Vol. 27, Supplement 12 (ed. A. Kent and J. G. Williams), Marcel Dekker, 1993, pp. 275--296. That article, in turn is a revision of an article entitled "Reasoning About Knowledge: An Overview" that appears in Theoretical Aspects of Reasoning Abou...