Algebraic proof theory for LE-logics

In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics). Specifically, we generalise the residuated frames in [16] to arbitrary signatures of normal lattice expansions (LE). Such a generalization provides a valuable tool for proving important properties of LE-logics in full uniformity. We prove semantic cut elimination for the display calculi D.LE associated with the basic normal LE-logics and their axiomatic extensions with analytic inductive axioms. We also prove the finite model property (FMP) for each such calculus D.LE, as well as for its extensions with analytic structural rules satisfying certain additional properties

Complexity results for some classes of strategic games

Game theory is a branch of applied mathematics studying the interaction of self-interested entities, so-called agents. Its central objects of study are games, mathematical models of real-world interaction, and solution concepts that single out certain outcomes of a game that are meaningful in some way. The solutions thus produced can then be viewed both from a descriptive and from a normative perspective. The rise of the Internet as a computational platform where a substantial part of today's strategic interaction takes place has spurred additional interest in game theory as an analytical tool, and has brought it to the attention of a wider audience in computer science. An important aspect of real-world decision-making, and one that has received only little attention in the early days of game theory, is that agents may be subject to resource constraints. The young field of algorithmic game theory has set out to address this shortcoming using techniques from computer science, and in particular from computational complexity theory. One of the defining problems of algorithmic game theory concerns the computation of solution concepts. Finding a Nash equilibrium, for example, i.e., an outcome where no single agent can gain by changing his strategy, was considered one of the most important problems on the boundary of P, the complexity class commonly associated with efficient computation, until it was recently shown complete for the class PPAD. This rather negative result for general games has not settled the question, however, but immediately raises several new ones: First, can Nash equilibria be approximated, i.e., is it possible to efficiently find a solution such that the potential gain from a unilateral deviation is small? Second, are there interesting classes of games that do allow for an exact solution to be computed efficiently? Third, are there alternative solution concepts that are computationally tractable, and how does the value of solutions selected by these concepts compare to those selected by established solution concepts? The work reported in this thesis is part of the effort to answer the latter two questions. We study the complexity of well-known solution concepts, like Nash equilibrium and iterated dominance, in various classes of games that are both natural and practically relevant: ranking games, where outcomes are rankings of the players; anonymous games, where players do not distinguish between the other players in the game; and graphical games, where the well-being of any particular player depends only on the actions of a small group other players. In ranking games, we further compare the payoffs obtainable in Nash equilibrium outcomes with those of alternative solution concepts that are easy to compute. We finally study, in general games, solution concepts that try to remedy some of the shortcomings associated with Nash equilibrium, like the need for randomization to achieve a stable outcome

Cooperating systems: Layered MAS

Distributed intelligent systems can be distinguished by the models that they use. The model developed focuses on layered multiagent system conceived of as a bureaucracy in which a distributed data base serves as a central means of communication. The various generic bureaus of such a system is described and a basic vocabulary for such systems is presented. In presenting the bureaus and vocabularies, special attention is given to the sorts of reasonings that are appropriate. A bureaucratic model has a hierarchy of master system and work group that organizes E agents and B agents. The master system provides the administrative services and support facilities for the work groups

Beyond semantic pollution: Towards a practice-based philosophical analysis of labelled calculi

This paper challenges the negative attitudes towards labelled proof systems, usually referred to as semantic pollution, by arguing that such critiques overlook the full potential of labelled calculi. The overarching objective is to develop a practice-based philosophical analysis of labelled calculi to provide insightful considerations regarding their proof-theoretic and philosophical value. To achieve this, successful applications of labelled calculi and related results will be showcased, and comparisons with other relevant works will be discussed. The paper ends by advocating for a more practice-based approach towards the philosophical understanding of proof systems and their role in structural proof theory

Practical Strategic Reasoning with Applications in Market Games.

Strategic reasoning is part of our everyday lives: we negotiate prices, bid in auctions, write contracts, and play games. We choose actions in these scenarios based on our preferences, and our beliefs about preferences of the other participants. Game theory provides a rich mathematical framework through which we can reason about the influence of these preferences. Clever abstractions allow us to predict the outcome of complex agent interactions, however, as the scenarios we model increase in complexity, the abstractions we use to enable classical game-theoretic analysis lose fidelity. In empirical game-theoretic analysis, we construct game models using empirical sources of knowledge—such as high-fidelity simulation. However, utilizing empirical knowledge introduces a host of different computational and statistical problems. I investigate five main research problems that focus on efficient selection, estimation, and analysis of empirical game models. I introduce a flexible modeling approach, where we may construct multiple game-theoretic models from the same set of observations. I propose a principled methodology for comparing empirical game models and a family of algorithms that select a model from a set of candidates. I develop algorithms for normal-form games that efficiently identify formations—sets of strategies that are closed under a (correlated) best-response correspondence. This aids in problems, such as finding Nash equilibria, that are key to analysis but hard to solve. I investigate policies for sequentially determining profiles to simulate, when constrained by a budget for simulation. Efficient policies allow modelers to analyze complex scenarios by evaluating a subset of the profiles. The policies I introduce outperform the existing policies in experiments. I establish a principled methodology for evaluating strategies given an empirical game model. I employ this methodology in two case studies of market scenarios: first, a case study in supply chain management from the perspective of a strategy designer; then, a case study in Internet ad auctions from the perspective of a mechanism designer. As part of the latter analysis, I develop an ad-auctions scenario that captures several key strategic issues in this domain for the first time.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75848/1/prjordan_1.pd