Samir Chopra

Relevance sensitive belief structures

We propose a new relevance sensitive model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agents ability to answer queries in a coherent way using Belnaps four‐valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally tractable procedures for query answering and belief base revision are obtained.

Knowledge-Theoretic Properties of Strategic Voting

Results in social choice theory such as the Arrow and Gibbard-Satterthwaite theorems constrain the existence of rational collective decision making procedures in groups of agents. The Gibbard-Satterthwaite theorem says that no voting procedure is strategy-proof. That is, there will always be situations in which it is in a voter’s interest to misrepresent its true preferences i.e., vote strategically. We present some properties of strategic voting and then examine – via a bimodal logic utilizing epistemic and strategizing modalities – the knowledge-theoretic properties of voting situations and note that unless the voter knows that it should vote strategically, and how, i.e., knows what the other voters’ preferences are and which alternate preference P′ it should use, the voter will not strategize. Our results suggest that opinion polls in election situations effectively serve as the first n–1 stages in an n stage election.

Social choice theory, belief merging, and strategy-proofness

Intelligent agents have to be able to merge informational inputs received from different sources in a coherent and rational way. Several proposals have been made for information merging in which it is possible to encode the preferences of sources [5,4,19,24,25,1]. Information merging has much in common with social choice theory, which aims to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection, frameworks for information merging should provide satisfactory resolutions of problems raised in social choice theory. We investigate the link between the merging of epistemic states and some results in social choice theory. This is achieved by providing a consistent set of properties-akin to those used in Arrows theorem [2]-for merging. It is shown that in this framework there is no Arrow-like impossibility result. By extending this to a consistent framework which includes properties corresponding to the notion of being strategy-proof, we show that results due to Gibbard and Satterthwaite [13,31,32] and others [6,3] do not hold in merging frameworks.

Relevance Sensitive Non-Monotonic Inference on Belief Sequences

We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the putative conclusion and formulas in the sequence. The relevance relations are ternary (using context as a parameter) as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely presented formalism and a plausible model of reasoning for automated agents.

Social Choice, Merging, and Elections

Intelligent agents have to be able to merge inputs received from different sources in a coherent and rational way. Recently, several proposals have been made for the merging of structures in which it is possible to encode the preferences of sources [5,4,12,13,14,1]. Information merging has much in common with the goals of social choice theory: to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection it seems reasonable to require that any framework for the merging of information has to provide satisfactory ways of dealing with the problems raised in social choice theory. In this paper we investigate the link between the merging of epistemic states and two important results in social choice theory. We show that Arrows well-known impossibility theorem [2] can be circumvented when the preferences of sources are represented in terms of epistemic states. This is achieved by providing a consistent set of properties for merging from which Arrow-like properties can be derived. We extend this to a consistent framework which includes properties corresponding to the notion of being strategy-proof. The existence of such an extended framework can be seen as a circumvention of the impossibility result of Gibbard and Satterthwaite [8,17,18] and related results [6, 3].

Syntactic Representations of Semantic Merging Operations

Recent research suggests the usefulness of conducting information merging on the level of epistemic states as an alternative to the usual approach of knowledge base merging [1,2]. We take an epistemic state to be an assignment of natural numbers to the classical valuations of the finite propositional logic under consideration. In this paper we investigate various syntactic representations of epistemic states and show how these can be employed to represent merging operations syntactically. These include ranked knowledge bases and their normals forms, as well as different versions of structures referred to as partitions. We show that there are efficient methods for transformaing any ranked knowledge base into an equivalent partition, and vice versa. We provide a uniform method for obtaining syntactic representations, in terms of partitions, of a large class of semantic merging operations. This method is linear in n times the product of the sizes of the n partitions used to represent the epistemic states to be merged. For the class of lexicographic merging operations, it can be proved that this method represents the best we can do in terms of computational complexity. We also show that the structure of some semantic merging operations can be exploited to obtain syntactic representations for them which can be determined much more efficiently than the uniform method provided. To be able to use these efficient methods, it is necessary to use ranked knowledge bases as the syntactic representational form.

Non-prioritised ranked belief change

Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories.

An experimental study comparing the effectiveness of computer graphics data versus computer tabular data

A number of studies that compare the effectiveness of data presented in graphic form versus data presented in tabular form have been performed. Results have been mixed. In a study by Dickson et al. (1986) that used business students as subjects it is suggested that task variables are paramount in the determination of such effectiveness. It is suggested that the type of data and type of subject used in the work by Dickson et al. favored tabular presentation and compromise any generalization of their conclusions. The current study finds that user training/expertise is a critical variable in determining the effectiveness of graphs versus tables. The conclusion drawn is that a user-friendly system should make both modes available so that the users have the option of selecting their preferred mode. >

Iterated Belief Change and the Recovery Axiom

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom.

Rights for autonomous artificial agents

The growing role of artificial agents necessitates modifying legal frameworks to better address human interests.