Daniel J. Lehmann

What does a conditional knowledge base entail

Abstract This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type if … then … , represents the explicit defeasible knowledge an agent has about the way the world generally behaves. We look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base. In a previous paper, Kraus and the authors defined and studied preferential consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures. This paper studies a more restricted class of consequence relations, rational relations. It is argued that any reasonable nonmonotonic inference procedure should define a rational relation. It is shown that the rational relations are exactly those that may be represented by a ranked preferential model, or by a (nonstandard) probabilistic model. The rational closure of a conditional knowledge base is defined and shown to provide an attractive answer to the question of the title. Global properties of this closure operation are proved: it is a cumulative operation. It is also computationally tractable. This paper assumes the underlying language is propositional.

Combinatorial auctions with decreasing marginal utilities

In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. While we show that the allocation problem among valuations with decreasing marginal utilities is NP-hard, we present an efficient greedy 2-approximation algorithm for this case. No such approximation algorithm exists in a setting allowing for complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.

Impartiality, Justice and Fairness: The Ethics of Concurrent Termination

The method of well founded structures for proving termination of programs is extended to concurrent programs. The more complicated case is when a program terminates only for fair executions. Different versions of fairness are introduced: Impartiality, Fairness and Justice, and Methods for proving their termination are presented.

On the advantages of free choice: a symmetric and fully distributed solution to the dining philosophers problem

It is shown that distributed systems of probabilistic processors are essentially more powerful than distributed systems of deterministic processors, i.e., there are certain useful behaviors that can be realized only by the former. This is demonstrated on the dining philosophers problem. It is shown that, under certain natural hypotheses, there is no way the philosophers can be programmed (in a deterministic fashion) so as to guarantee the absence of deadlock (general starvation). On the other hand, if the philosophers are given some freedom of choice one may program them to guarantee that every hungry philosopher will eat (with probability one) under any circumstances (even an adversary scheduling). The solution proposed here is fully distributed and does not involve any central memory or any process with which every philosopher can communicate.

Another perspective on default reasoning

The lexicographic closure of any given finite setD of normal defaults is defined. A conditional assertiona ❘∼b is in this lexicographic closure if, given the defaultsD and the facta, one would concludeb. The lexicographic closure is essentially a rational extension ofD, and of its rational closure, defined in a previous paper. It provides a logic of normal defaults that is different from the one proposed by R. Reiter and that is rich enough not to require the consideration of non-normal defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiters logic of defaults.

Optimal solutions for multi-unit combinatorial auctions: branch and bound heuristics

Finding optimal solutions for multi-unit combinatorial auctions is a hard problem and finding approximations to the optimal solution is also hard. We investigate the use of Branch-and-Bound techniques: they require both a way to bound from above the value of the best allocation and a good criterion to decide which bids are to be tried first. Different methods for efficiently bounding from above the value of the best allocation are considered. Theoretical original results characterize the best approximation ratio and the ordering criterion that provides it. We suggest to use this criterion.

DESIGNING AND BUILDING A NEGOTIATING AUTOMATED AGENT

Negotiations are very important in a multiagenl environment, particularly, in an environment where there are conflicts between the agents, and cooperation would be beneficial. We have developed a general structure for a Negotiating Automated Agent that consists of five modules: a Prime Minister, a Ministry of Defense, a Foreign Office, a Headquarters and Intelligence. These modules are implemented using a dynamic set of local agents belonging to the different modules. We used this structure to develop a Diplomacy player. Diplomat. Playing Diplomacy involves a certain amount of technical skills as in other board games, but the capacity to negotiate, explain, convince, promise, keep promises or break them, is an essential ingredient in good play. Diplomat was evaluated and consistently played better than human players.

Algebraic specification of data types: A synthetic approach

A mathematical interpretation is given to the notion of a data type, which allows procedural data types and circularly defined data types. This interpretation seems to provide a good model for what most computer scientists would call data types, data structures, types, modes, clusters or classes. The spirit of this paper is that of McCarthy [43] and Hoare [18]. The mathematical treatment is the conjunction of the ideas of Scott on the solution of domain equations [34], [35], and [36] and the initiality property noticed by the ADJ group (ADJ [2] and [3]). The present work adds operations to the data types proposed by Scott and proposes an alternative to the equational specifications proposed by Guttag [14], Guttag and Horning [15] and ADJ [2]. The advantages of such a mathematical interpretation are the following: throwing light on some ill-understood constructs in high-level programming languages, easing the task of writing correct programs and making possible proofs of correctness for programs or implementations.

Modeling compositionality by dynamic binding of synfire chains.

This paper examines the feasibility of manifesting compositionality by a system of synfire chains. Compositionality is the ability to construct mental representations, hierarchically, in terms of parts and their relations. We show that synfire chains may synchronize their waves when a few orderly cross links are available. We propose that synchronization among synfire chains can be used for binding component into a whole. Such synchronization is shown both for detailed simulations, and by numerical analysis of the propagation of a wave along a synfire chain. We show that global inhibition may prevent spurious synchronization among synfire chains. We further show that selecting which synfire chains may synchronize to which others may be improved by including inhibitory neurons in the synfire pools. Finally we show that in a hierarchical system of synfire chains, a part-binding problem may be resolved, and that such a system readily demonstrates the property of priming. We compare the properties of our system with the general requirements for neural networks that demonstrate compositionality.

Distance Semantics for Belief Revision

A vast and interesting family of natural semantics for Belief Revision is defined. Suppose one is given a distance d between any two models. One may define the revision of a theory K by a formula a as the theory defined by the set of all those models of a that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.