Agent's Beliefs Research Articles

The intentional stance as structure learning: a computational perspective on mindreading.

Recent theories of mindreading explain the recognition of action, intention, and belief of other agents in terms of generative architectures that model the causal relations between observables (e.g., observed movements) and their hidden causes (e.g., action goals and beliefs). Two kinds of probabilistic generative schemes have been proposed in cognitive science and robotics that link to a "theory theory" and "simulation theory" of mindreading, respectively. The former compares perceived actions to optimal plans derived from rationality principles and conceptual theories of others' minds. The latter reuses one's own internal (inverse and forward) models for action execution to perform a look-ahead mental simulation of perceived actions. Both theories, however, leave one question unanswered: how are the generative models - including task structure and parameters - learned in the first place? We start from Dennett's "intentional stance" proposal and characterize it within generative theories of action and intention recognition. We propose that humans use an intentional stance as a learning bias that sidesteps the (hard) structure learning problem and bootstraps the acquisition of generative models for others' actions. The intentional stance corresponds to a candidate structure in the generative scheme, which encodes a simplified belief-desire folk psychology and a hierarchical intention-to-action organization of behavior. This simple structure can be used as a proxy for the "true" generative structure of others' actions and intentions and is continuously grown and refined - via state and parameter learning - during interactions. In turn - as our computational simulations show - this can help solve mindreading problems and bootstrap the acquisition of useful causal models of both one's own and others' goal-directed actions.

Incentives for Learning

We analyze a dynamic principal-agent problem with moral hazard and private learning. Each period the agent faces a choice between two actions: a safe action with known returns (exploitation) and a costly risky action with unknown returns (experimentation). We explicitly characterize the cheapest time-dependent wage contracts implementing an action sequence by the agent consisting of a mix of risky and safe actions. We show that the wages for experimentation must be increasing to compensate for the agent's pessimistic beliefs whereas the wages for exploitation are driven by distinct upper bounds. The model's predictions have some empirical support.

Stochastic Choice and Optimal Sequential Sampling

We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. In the resulting optimal policy, the agent's choices are more likely to be correct when the agent chooses to decide quickly, provided that the agent's prior beliefs are correct. For this reason it better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model, where the agent is uncertain which of two actions is best but knows the utility difference between them.

Gurus and belief manipulation

We analyze a model with two types of agents: standard agents and gurus, i.e. agents who have the ability to influence the other investors. Gurus announce their beliefs and act accordingly. Gurus are strategic: they take into account the impact of their announced beliefs on the other agents, hence on prices. Standard agents observe gurus' performances, choose a guru and follow her/his recommendations. Prices are determined through a classical Walras mechanism. The competition among gurus for attracting followers among standard agents is governed by the level of accuracy of their predictions. The strategic behavior leads to belief subjectivity and heterogeneity among the gurus even when gurus' initial beliefs coincide with the objective belief. Optimism as well as pessimism can both emerge. We find a positive correlation across the agents between pessimism and risk tolerance. The representative agent belief, or the consensus belief is pessimistic. As a consequence of the pessimistic bias at the aggregate level, the risk premium is greater than in the standard rational expectations equilibrium. We show on an example that this impact is significative. In a multi-asset framework, the impact is stronger on the riskier assets.

Practical Extraction of Evidence Terms From Common-knowledge Reasoning

Knowledge, belief, and evidence are fundamental notions which appear in a wide range of areas. Over the last decade epistemic reasoning with justifications has broadened even more the scope of applications of epistemic logic as agents gained the ability to not only reason about epistemic states of knowledge and belief of agents, but also to track their justifications and to sort those which are pertinent to given facts and sufficient for epistemic conclusions.This paper extends realization algorithm for S4-to-LP case to S4nJ-to-S4nLP case. It converts cut-free derivations in S4nJ into derivations in the corresponding Justification Logic S4nLP where witnesses of knowledge, the justification terms, are recovered for all instances of justified common knowledge. The algorithm was implemented in the MetaPRL framework and was tested on several well-known epistemic puzzles, such as Muddy Children, Surprise Examination Paradox, etc.

Planning Over Multi-Agent Epistemic States: A Classical Planning Approach

Many AI applications involve the interaction of multiple autonomous agents, requiring those agents to reason about their own beliefs, as well as those of other agents. However, planning involving nested beliefs is known to be computationally challenging. In this work, we address the task of synthesizing plans that necessitate reasoning about the beliefs of other agents. We plan from the perspective of a single agent with the potential for goals and actions that involve nested beliefs, non-homogeneous agents, co-present observations, and the ability for one agent to reason as if it were another. We formally characterize our notion of planning with nested belief, and subsequently demonstrate how to automatically convert such problems into problems that appeal to classical planning technology. Our approach represents an important first step towards applying the well-established field of automated planning to the challenging task of planning involving nested beliefs of multiple agents.

Nonparametric Scoring Rules

A scoring rule is a device for eliciting and assessing probabilistic forecasts from an agent. When dealing with continuous outcome spaces, and absent any prior insights into the structure of the agent's beliefs, the rule should allow for a flexible reporting interface that can accurately represent complicated, multi-modal distributions. In this paper, we provide such a scoring rule based on a nonparametric approach of eliciting a set of samples from the agent and efficiently evaluating the score using kernel methods. We prove that sampled reports of increasing size converge rapidly to the true score, and that sampled reports are approximately optimal. We also demonstrate a connection between the scoring rule and the maximum mean discrepancy divergence. Experimental results are provided that confirm rapid convergence and that the expected score correlates well with standard notions of divergence, both important considerations for ensuring that agents are incentivized to report accurate information.

On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent's rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer set programming, fuzzy autoepistemic logic generalizes fuzzy answer set programming as well. Besides being related to answer set programming, autoepistemic logic is also closely related to several modal logics. To investigate whether a similar relationship holds in a fuzzy logical setting, we firstly generalize the main modal logics for belief to the setting of finitely-valued Łukasiewicz logic with truth constants Łkc, and secondly we relate them with fuzzy autoepistemic logics. Moreover, we show that the problem of satisfiability checking in these logics is NP-complete. Finally, we generalize Levesque's results on stable expansions, belief sets, and “only knowing” operators to our setting, and provide a complete axiomatization for a logic of “only knowing” in the Łkc framework.

Preferences for Flexibility and Randomization under Uncertainty

An uncertainty-averse agent prefers betting on an event whose probability is known, to betting on an event whose probability is unknown. Such an agent may randomize his choices to eliminate the effects of uncertainty. For what sort of preferences does a randomization eliminate the effects of uncertainty? To answer this question, we investigate an agent's preferences over sets of acts. We axiomatize a utility function, through which we can identify the agent's subjective belief that a randomization eliminates the effects of uncertainty. (JEL D11, D81)

Robot location estimation in the situation calculus

Location estimation is a fundamental sensing task in robotic applications, where the world is uncertain, and sensors and effectors are noisy. Most systems make various assumptions about the dependencies between state variables, and especially about how these dependencies change as a result of actions. Building on a general framework by Bacchus, Halpern and Levesque for reasoning about degrees of belief in the situation calculus, and a recent extension to it for continuous probability distributions, in this paper we illustrate location estimation in the presence of a rich theory of actions using examples. The formalism also allows specifications with incomplete knowledge and strict uncertainty, as a result of which the agent's initial beliefs need not be characterized by a unique probability distribution. Finally, we show that while actions might affect prior distributions in nonstandard ways, suitable posterior beliefs are nonetheless entailed as a side-effect of the overall specification.

A belief revision framework for revising epistemic states with partial epistemic states

Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.

A formal account of dishonesty

This article provides formal accounts of dishonest attitudes of agents. We introduce a propositional multi-modal logic that can represent an agent's belief and intention as well as communication between agents. Using the language, we formulate different categories of dishonesty. We first provide two different definitions of lies and provide their logical properties. We then consider an incentive behind the act of lying and introduce lying with objectives. We subsequently define bullshit, withholding information and half-truths, and analyse their formal properties. We compare different categories of dishonesty in a systematic manner, and examine their connection to deception. We also propose maxims for dishonest communication that agents should ideally try to satisfy.

Heuristic learning in intraday trading under uncertainty

Until recently economists focused on structural models that were constrained by a lack of high-frequency data and theoretical deficiencies. Little academic research has been invested in actually trying to build successful real-time trading models for the high-frequency foreign exchange market, which is characterized by inherent complexity and heterogeneity. The present work opens new directions for inference on market efficiency in an attempt to account for the use of technical analysis by practitioners over many years now. This paper presents a heuristic model that efficiently emulates the dynamic learning of intraday traders. The proposed setup incorporates agent beliefs, preferences and expectations while it integrates the calibration of technical rules by means of adaptive training. The study focuses on EUR/USD which is the most liquid and widely traded currency pair. The data consist of a very large tick-by-tick sample of bid and ask prices covering many trading periods to enhance robustness in the results. The efficiency of a technical trading strategy based on the proposed model is investigated in terms of directional predictability. The heuristic learning system is compared against many non-linear models, a random walk and a buy & hold strategy. Based on statistical testing it is shown that, with the inclusion of transaction costs, the profitability of the new model is consistently superior. These findings provide evidence of technical predictability under incomplete information and can be justified by invoking the existence of heterogeneity caused by many factors affecting market microstructure. Overall, the results suggest that the proposed model can be used to improve upon traditional technical analysis approaches. • Little academic research exists in real-time trading for high-frequency FX rates. • Model incorporates beliefs, preferences & expectations via adaptive training. • Heuristic adaptive learning system is compared against many models. • Including transaction costs the profitability of the model is consistently superior. • Findings provide evidence of technical predictability under incomplete information.

Beliefs and actions in the trust game: Creating instrumental variables to estimate the causal effect

In many economic contexts, an elusive variable of interest is the agent's belief about relevant events, e.g. about other agents' behavior. A growing number of surveys and experiments asks participants to state beliefs explicitly but little is known about the causal relation between beliefs and actions. This paper discusses the possibility of creating exogenous instrumental variables for belief statements, by informing the agent about exogenous manipulations of the relevant events. We conduct trust game experiments where the amount sent back by the second player (trustee) is exogenously varied. The procedure allows detecting causal links from beliefs to actions under plausible assumptions. The IV-estimated effect is significant, confirming the causal role of beliefs.

How Corporations Overcome Issue Illegitimacy and Issue Equivocality to Address Social Welfare: The Role of the Social Change Agent

While corporations are increasingly being called on to improve social welfare, researchers have primarily focused their efforts on the role of external pressures and top managers in shaping a corporation’s engagement with social issues. As an alternative, I consider the role of social change agents who work within corporations and direct their firms to address a social issue. I suggest two issue impediments obstructing these efforts—issue illegitimacy and issue equivocality—that are shaped by economic philosophies, institutional fields, firm missions, and social change agent beliefs. These impediments ground four types of issues that social change agents attempt to advance: convertible, blurry, safe, and risky. I propose meaning-making tactics best suited to address the type of social issue individuals seek to advance inside a firm: framing, labeling, maintaining, and importing. I argue that by matching the issue type and meaning-making tactic, social change agents will more likely influence top managers to support a social issue. This article contributes to the literature by explaining how meaning making serves at the heart of impediments to and potential solutions to firms’ efforts to improve social welfare and by spotlighting the role of a firm’s employees in encouraging the organization to improve social welfare.

Measuring Inconsistency in Multi-Agent Systems

We introduce and investigate formal quantitative measures of inconsistency between the beliefs of agents in multi-agent systems. We start by recalling a well-known model of belief in multi-agent systems, and then, using this model, present two classes of inconsistency metrics. First, we consider metrics that attempt to characterise the overall degree of inconsistency of a multi-agent system in a single numeric value, where inconsistency is considered to be individuals within the system having contradictory beliefs. While this metric is useful as a high-level indicator of the degree of inconsistency between the beliefs of members of a multi-agent system, it is of limited value for understanding the structure of inconsistency in a system: it gives no indication of the sources of inconsistency. We therefore introduce metrics that quantify for a given individual the extent to which that individual is in conflict with other members of the society. These metrics are based on power indices, which were developed within the cooperative game theory community in order to understand the power that individuals wield in cooperative settings.

Supernatural punishment, in-group biases, and material insecurity: experiments and ethnography from Yasawa, Fiji

Threat of supernatural punishment can promote prosociality in large-scale societies; however, its impact in smaller societies with less powerful deities is less understood. Also, while perceived material insecurity has been associated with increasing religious belief, the relationships between insecurity, supernatural punishment beliefs, and prosocial behavior are unclear. In this study, we explore how material insecurity moderates the supernatural punishment beliefs that promote different expectations about distant, anonymous strangers among a sample of villagers living in Yasawa, Fiji. We examined this relationship by employing an economic game designed to measure local recipient favoritism vs. egalitarian, rule-following behavior. Using indices of three different “punishing” agents – the Christian God (“Bible God”), the deified ancestors (Kalou-vu), and the police – we find that increased belief in Bible God punishment predicts less local recipient favoritism at low and moderate but not high material insecurity. Punishing Kalou-vu also predicts less favoritism at low and moderate insecurity, but more favoritism at high insecurity. Police punishment poorly predicts favoritism, suggesting that secular authority has less impact on isolated communities. We discuss implications for understanding how different kinds of supernatural and secular agent beliefs impact prosocial behavior.

Social learning with time-varying weights

This paper investigates a non-Bayesian social learning model, in which each individual updates her beliefs based on private signals as well as her neighbors’ beliefs. The private signal is involved in the updating process through Bayes’ rule, and the neighbors’ beliefs are embodied in through a weighted average form, where the weights are time-varying. The authors prove that agents eventually have correct forecasts for upcoming signals, and all the beliefs of agents reach a consensus. In addition, if there exists no state that is observationally equivalent to the true state from the point of view of all agents, the authors show that the consensus belief of the whole group eventually reflects the true state.

An argumentation-based approach for reasoning about trust in information sources

During a dialogue, agents exchange information with each other and need thus to deal with incoming information. For that purpose, they should be able to reason effectively about trustworthiness of information sources. This paper proposes an argument-based system that allows an agent to reason about its own beliefs and information received from other sources. An agent's beliefs are of two kinds: beliefs about the environment (like the window is closed) and beliefs about trusting sources (like agent i trusts agent j). Six basic forms of trust are discussed in the paper including the most common one on sincerity. Starting with a base which contains such information, the system builds two types of arguments: arguments in favour of trusting a given source of information and arguments in favour of believing statements which may be received from other agents. We discuss how the different arguments interact and how an agent may decide to trust another source and thus to accept information coming from that source....

Realizing public announcements by justifications

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present OPAL(K) and JPAL(K), two alternative justification counterparts of Gerbrandy–Groeneveld's public announcement logic PAL(K). We show that PAL(K) is the forgetful projection of both OPAL(K) and JPAL(K). We also establish that JPAL(K) partially realizes PAL(K). The question whether a similar result holds for OPAL(K) is still open.