Agent's Beliefs Research Articles

Heuristics, justification, and defeasible reasoning

Heuristics can be regarded as justifying the actions and beliefs of problem-solving agents. I use an analysis of heuristics to argue that a symbiotic relationship exists between traditional epistemology and contemporary artificial intelligence. On one hand, the study of models of problem-solving agents usingquantitative heuristics, for example computer programs, can reveal insight into the understanding of human patterns of epistemic justification by evaluating these models' performance against human problem-solving. On the other hand,qualitative heuristics embody the justifying ability of defeasible rules, the understanding of which is provided by traditional epistemology.

Subjective Probability Without Monotonicity: or How Machina's Mom May Also be Probabilistically Sophisticated

If an agent's preferences over subjectively uncertain acts are consistent with his or her having a subjective probability distribution over the states of nature, then those preferences can induce consistent preferences over «objectively» risky lotteries. Such «probabilistically sophisticated» behavior thus allows us to treat decision making under situations of uncertainty in an analogous manner to those under risk. This paper first characterizes exactly what probabilistic sophistication entails for an agent's beliefs about the likelihood of states of nature. Secondly, it presents characterizations of probabilistically sophisticated individuals whose induced lottery preferences obey neither the Independence AXiom (unlike Savage (1954, 1972)) nor a monotonicity property that shares some of the nature of Independence (unlike Machina and Schmeidler (1992))

Multiagent reasoning with probability, time, and beliefs

Any agent interacting with the real world must be able to reason about uncertainty in the world, about the actions that may occur in the world (either due to the agent or those initiated by other agents), about the (probabilistic) beliefs of other agents, and how these (probabilistic) beliefs are changing over time. In this article, we develop a family of logics that a reasoning agent may use to perform successively more sophisticated types of reasoning in such environments. We also characterize different types of agents. Furthermore, we provide a logic that enables a systems designer (who may have populated an environment with a collection of such autonomous agents) to reason about the system of agents as a whole. © 1995 John Wiley & Sons, Inc.

On rational belief equilibria

We study equilibria in which agent's belief are rational in the sense of Kurz [1994]. The market is formulated by specifying a stochastic demand function and a continuum of producers, each with a quadratic cost function who must select their output before knowing prices. Holding Rational Beliefs about future prices, producers maximize expected profits. In a Rational Belief Equilibrium (RBE) agents select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data. It is shown that there exists a continuum of RBE's and they could entail very different patterns of time series for the economy and consequently different aggregate levels of longterm volatility. Since the model contains exogenously specified random variables, the difference in the level of long-term volatility of prices among the different RBE's arises endogenously as an “amplification” of the volatility of exogenous variables. The paper derives exact bounds on the possible levels of such “amplification.”

Relating only knowing to minimal belief and negation as failure

Abstract In this paper, we relate Lifschitz's logic of minimal belief and negation as failure (MBNF) to Levesque's logic of only knowing (OL). MBNF can be viewed as an integration of Lin and Shoham's logic of grounded knowledge and the theory of epistemic queries by Levesque and Reiter. Lifschitz showed that MBNF can be used as a general framework to compare different non-monotonic formalisms such as default logic and circumscription, as well as several forms of logic programs, including disjunctive logic programs with classical negation. Levesque's logic of only knowing is an epistemic formalism which can be used to model agent's knowledge and belief and to answer epistemic queries. The OL logic allows one to express the statement φ is all that is known'. Levesque showed that autoepistemic logic of Moore can be embedded in OL and he also gave a proof theory for OL. We show that a substantial subset of propositional MBNF can be embedded in OL (and hence in autoepistemic logic). In particular, the class of...

MAKRS: a knowledge and belief representation system for multiple agents

The paper presents a knowledge and belief representation system for multiple agents called MAKRS. MAKRS can represent and reason about multi-agent knowledge and belief as well as factual knowledge of the actual world. It can also process some axions which are usually used to represent the characteristics of each agent's knowledge and belief. MAKRS can be used as a tool to construct knowledge bases for various applications where multiple agents co-exist, and some sample knowledge bases are constructed to demonstrate its usefulness and practicality.

Intertemporal Asset Pricing with Heterogeneous Beliefs

We examine the behaviour of the interest rate, asset prices, and asset holdings in an economy with heterogeneous, rationally updated beliefs about the expected rate of production growth. The equilibrium interest rate is a weighted average of the interest rates that would prevail in economies populated by homogeneous agents with the beliefs of the respective agents in the heterogeneous model. The weights are given by the fractions of total wealth held. Financial innovation affects the dynamics of allocations and prices but preserves the aggregate output process and the structure of equilibrium: asset prices also display the wealth-weighted average characterization. Journal of Economic Literature Classification Numbers: C60, D52, D91, G12.

Problems with persistence

A fundamental question in reasoning about change is, what information does a reasoning agent infer about later times from earlier times? I will argue that reasoning about change by an agent is to be modeled in terms of the persistence of the agent's beliefs over time rather than the persistence of truth and that such persistence is explained by pragmatic factors about how agents acquire information from other agents rather than by general principles of persistence about states of the world. AI accounts of persistence have focused on ‘closed world’ examples of change, in which the agent believes that the truth of a proposition is unaltered so long as he or she has no evidence that it has been changed. AI principles of persistence seem plausible in a closed world where one assumes the agent knows everything that is happening. If one drops the assumption of omniscience, however, the analysis of persistence is implausible. To get a good account of persistence and reasoning about change, I argue we should examine ‘open world’ examples of change, in which the agent is ignorant of some of the changes occurring in the world. In open world examples of change, persistence must be formulated, I argue, as a pragmatic principle about the persistence of beliefs. After elaborating my criticisms of current accounts of persistence, I examine how such pragmatic principles fare with the notorious examples of reasoning about action that have collectively characterized the so-called frame problem.

A model of belief

The paper provides a mathematical model of an agent's belief in an event by identifying it with his ability to imagine the event within the context of his previous experience. This approach leads to belief having properties different from those normally ascribed to it.

Structural and functional quantization of vagueness

This paper proposes two methods of quantizing vague categories in terms of quantities whose identities have been either widely recognized in the fuzzy set theory literature or established by Bayesian Decision Theory. The methods are called structural quantization and functional quantization respectively. The idea behind structural quantization is that for a ‘comparative’ vague category like good-scores, there exists a preference ordering among the possible scores and how good a particular score is depends on how large the portion of examinees whose scores are lower than that score is. Functional quantization adopts the conclusion of Bayesian Decision Theory that a rational agent's belief can be represented by a probability. To quantize the term good-score, the method first assesses the two probabilities that respectively represent a rational agent's beliefs about John's score before and after learning that “John has got a good-score”. It then derives a membership function by comparing those two probabilities. The equivalence of the two quantization methods is hypothesized. The logic connectives ‘not’, ‘and’ and ‘or’ are discussed in the setting of structural quantization, while aggregation of information is addressed in the setting of functional quantization.

Bidding behaviour in OCS drainage auctions: Theory and evidence

Empirical economists frequently criticize game-theoretic models of markets on the grounds that they fail to generate empirically testable hypotheses. The complaint is that prices and quantities, or entry decisions, are explained using factors that are not observable to the econometrician, such as private valuations and beliefs of agents. The corollary to this argument is that the only way to proceed empirically is through experiments. However. this approach suffers from the problem that the experience of the subjects may be too limited and the compensation too small for them to perform the requisite optimizing calculations. The objective of this paper is to discuss the above criticism of gametheoretic models in the context of our work on markets of offshore oil and gas leases. In this case study, one group of buyers is better informed about the unknown value of the leaae being sold that another group, and the two groups can be identified. Game-theoretic models of markets with informational asymmetries generate restrictions on the relative behaviour and performance of the two groups of buyers. and some of these restrictions are empirically testable. We examine them using bid and profit data. More generally, the work serves to illustrate a basic point about testing models of

Deductive efficiency, belief revision and acting

Abstract The SNePS inference engine is optimized for deductive efficiency, i.e. all beliefs acquired via inference are added to the agent's beliefs so that future queries may be answered by a retrieval rather than rederivation. An assumption-based truth maintenance system keeps track of the derivation histories of derived beliefs. We show how such an architecture simplifies the ontology of prepositional representations of plans; acts; preconditions, and effects of actions. In addition, the deductive efficiency of the basic system automatically extends itself to efficient search of plans, and hierarchical plan decompositions.

Propositionally representing incomplete knowledge about existence

Abstract This paper considers the problem of representing the knowledge state of an observed agent who has incomplete knowledge of existence. Agents in such knowledge states are said to have existential misconceptions. We describe preliminary work on representing the knowledge state of an agent who possesses existential misconceptions and how to detect when this occurs. The method is based on a simulation of the observed agent's processes of information acquisition. We describe an implementation of this system and study its operation in a simulated microworld. The agent's acquisition of existential misconceptions is correlated with the agent's inaccurate beliefs of equality. This makes it possible to characterize an agent's existential misconceptions by describing its inaccurate beliefs of equality.

Justification and the Will

Reasons for intending are the psychological states which rationalise and explain our intentions. Reasons for intending to do act A, says Davidson (1985), are reasons for doing A. They are desires for ends E and beliefs that doing A would further E, and the further psychological states that provide reasons for such desires and beliefs. Practical deliberation is simply about how to act. I have urged otherwise. I have claimed (1991) that reasons for intending to do A are desires for ends E and beliefs that now intending to do A would further E, and the further psychological states that provide reasons for such desires and beliefs. Practical deliberation is also about what to intend. Mele, in a helpful reply (1992), trims. He argues that though I show Davidson's account of reasons for intending to be false for some cases, there are other cases where it is true. Mele produces two types of case. The first type of casean adult case-is a case of ordinary deliberation, where an adult agent takes it for granted that her intention to do A will lead to A's being done. In such a case the agent's beliefs about what ends intending to do A would further may remain in the psychological background. These beliefs need not be amongst the states which actually explain her intention. The agent simply forms her intention on the basis of her beliefs about what ends doing A would further. The second type of case-a toddler case-is where a toddler acts intentionally. Mele supposes that we should infer from the toddler's intentional actions to its possession of intentions which explain those actions. He then claims that since a toddler won't hold beliefs about what ends its intentions would further, intentional toddler agency provides a counterexample to my theory of intention. Let me concede the truth of Mele's claim that adult cases are perfectly possible: Davidson's story about how intentions are rationalised and explained is not false in every case of intention. But on what is the issue of substance the nature of intentions themselves-honours are not even between Davidson and me. The model of intention that lies behind Davidson's account of reasons for intending is still discredited, and my model is still established. Secondly, toddler cases are not so clear as Mele makes out. For on my model of intention or even on Davidson's, for that matter-it's far from obvious that, as Mele puts it,

On Perfect Introspection with Quantifying-In1

Agents with perfect introspection may have incomplete beliefs about the world, but they possess complete knowledge about their own beliefs. This fact suggests that the beliefs of introspective agents should be completely determined by their objective beliefs, that is, those beliefs that are only about the domain in question and not about other beliefs. Introspection and logical reasoning alone should suffice to reconstruct all other beliefs from the objective ones. While this property has been shown to hold for propositional belief logics, there have so far only been negative results in the case of first-order belief logics with quantifying-in. In this paper we present a logic of belier with quantifying-in, where the beliefs of a perfectly introspective agent are indeed uniquely determined by the objective beliefs. The result is obtained by weakening the notion of belief of an existing logic that does not have this property.

Backward induction and beliefs about oneself

According to decision theory, the rational initial action in a sequential decision-problem may be found by ‘backward induction’ or “folding back’. But the reasoning which underwrites this claim appeals to the agent's beliefs about what she will later believe, about what she will later believe she will still later believe, and so forth. There are limits to the ‘depth’ of people's beliefs. Do these limits pose a threat to the standard theory of rational sequential choice? It is argued, first, that the traditional solutions of certain games depend on knowledge which exceeds depth limits, and that these solutions therefore cannot be shown rational in the usual sense. Then, for that related reason even ‘folding back’ solutions of one-person problems cannot be! A revision of our notion of rational choice is proposed, analogous to the reliabilist account of knowledge of Goldman and others, by which this paradox is resolved.

An Objectivist's Guide to Subjective Value

Oedipus killed his father and made love to his mother. Accepting Greek, and conventional, views on the morality of patricide and incest, Oedipus acted wrongly on both counts. But that is not the whole of the story. For it was precisely in the attempt to avoid these very wrongs that Oedipus so acted, believing in the light of the best evidence available to him that he was successfully avoiding them. Cases like this lead us naturally to a familiar distinction: between the objective and subjective notions of moral rightness. But which, if either, of these two notions is the primary one for moral theory, and what exactly are the relations between them? We address this question from within a broadly consequentialist framework, arguing for a version of objectivism which explains and justifies subjectivism where it is right and corrects it where it is wrong. According to the consequentialist, the moral rightness of an option is related in some way to the value of its consequences. A major problem for the consequentialist is to explain the nature of this relation. In particular, is the morally right action the one with the best consequences, or is the morally right action the one which is best in the light of the agent's beliefs? The subjectivist claims that the primary notion for moral theory is given by what is best by the agent's lights (or, as we will say, what has greatest subjective value) regardless of what is actually the best. 1 The objectivist claims that the primary notion for moral theory is given by what is best (or, as we will say, what has greatest objective value) regardless of how things seem to the agent.2

THE NATURE OF RATIONAL CHOICE AND THE FOUNDATIONS OF STATISTICS *

This paper addresses the claim that L. J. Savage's account of subjective utility theory models beliefs for all rational agents. Proposals for a two-dimensional model of belief are discussed and sources of criticism of subjective utility theory as a theory of rational choice are categorized. A theory of rational choice is proposed that gives conditions under which choices (including those made by uncertainty averters) can be judged to be rational. The paper corroborates A. K. Sen's findings, which show that rationality is not a behavioral entity. Copyright 1991 by Royal Economic Society.

Belief ascription, metaphor, and intensional identification

This article discusses the extension of ViewGen, an algorithm derived for belief ascription, to the areas of intensional object identification and metaphor. ViewGen represents the beliefs of agents as explicit, partitioned proposition sets known as environments. Environments are convenient, even essential, for addressing important pragmatic issues of reasoning. The article concentrates on showing that the transfer of information in metaphors, intensional object identification, and ordinary, nonmetaphorical belief ascription can all be seen as different manifestations of a single environment-amalgamation process. The article also briefly discusses the extension of ViewGen to speech-act processing and the addition of a heuristic-based, relevance-determination procedure, and justifies the partitioning approach to belief ascription.

A sense-based, process model of belief

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for ‘nested intensional model’) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, NIM provides agents with a conceptual map, interrelating the concepts of ‘knowledge’, ‘belief’, ‘truth’, and a number of cognate concepts, such as ‘infers’, ‘retracts’, and ‘questions’. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, ℐ-FOL (presented herein). ℐ-FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, ℐ-FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of ℐ-FOL and NIM to interagent reasoning are described and the soundness and completeness of ℐ-FOL are established herein.