Papers by Aleks Knoks
Backward and forward induction can be viewed as two styles of reasoning in dynamic games. Since e... more Backward and forward induction can be viewed as two styles of reasoning in dynamic games. Since each prescribes taking a different attitude towards the past moves of the other player(s), the strategies they identify as rational are sometimes incompatible. Our goal is to study players who are able to deliberate between backward and forward induction, as well as conditions under which one is superior to the other. This extended abstract is our first step towards this goal. We present an extension of Stalnaker's game models, in which the players can make ``trembling hand'' mistakes. This means that when a player observes an unexpected move, she has to figure out whether it is a result of a deliberate choice or a mistake, thereby committing herself to one of the two styles of reasoning.
Short version published as: Alama J., Knoks A., & Uckelman S. L. "Dialogue games for classical logic", in Giese M. & Kuznets R., TABLEAUX 2011: Workshops, Tutorials, and Short Papers, Technical Report IAM-11-002 (Universität Bern): 82--86, 2011
We define a class of dialogue games and prove that existence of winning strategies for the Propone... more We define a class of dialogue games and prove that existence of winning strategies for the Proponent in this class of games corre- sponds to validity in classical propositional logic. Many authors have stated similar results without actually proving the correspondence. We modify the proof for intuitionistic logic given by Fermuller [3], improving his proof along the way. Fermuller also defines a class of dialogue games that capture classical validity. We employ standard dialogue games and a standard sequent calculus for classical logic; our proof thus differs from Fermuller’s by avoiding his use of parallel dialogue games and hyper- sequents. The result is a substantially simpler correspondence between dialogue games and classical logic.
Dialogue semantics for logic are two-player logic games between a Pro- ponent who puts forward a... more Dialogue semantics for logic are two-player logic games between a Pro- ponent who puts forward a logical formula ϕ as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which different logics can be obtained through only small variations of the basic rules. We introduce the composition problem for dialogue games as the problem of resolving, for a set S of rules for dialogue games, whether the set of S-dialogically valid formulas is closed under modus ponens. Solving the composition problem is fundamental for the dialogical approach to logic; despite its simplicity, it often requires an indirect solution with the help of significant logical machinery such as cut-elimination. Direct solutions to the composition problem can, however, some- times be had. As an example, we give a set N of dialogue rules which is well-justified from the dialogical point of view, but whose set N of dialogically valid formulas is both non-trivial and non-standard. We prove that the composition problem for N can be solved directly, and introduce a tableaux system for N.
Drafts by Aleks Knoks
centria.di.fct.unl.pt
Abstract. In this paper we develop a tableau system for the dialogical logic N, introduced in [1]... more Abstract. In this paper we develop a tableau system for the dialogical logic N, introduced in [1], which is defined as the set of formulas for which there is a winning strategy for the Proponent according to a certain set of dialogical rules. We prove the soundness and completeness of this tableau system with respect to the dialogue semantics for the logic, thus giving it an alternative characterization.
Deontic conflicts pose an important challenge to deontic logicians. The standard account —standard... more Deontic conflicts pose an important challenge to deontic logicians. The standard account —standard deontic logic, SDL— is not apt for addressing this challenge since it trivializes conflicts. Two main stratagems for gaining conflict-tolerance have been proposed: to weaken SDL in various ways, and to contextualize the reign of SDL to consistent subsets of the premise set. The latter began with the work of van Fraassen and has been further developed by Horty. In this paper we characterize this second ap- proach in general terms. We also study three basic ways to contextualize SDL and supplement each of these with a dynamic proof theory in the framework of adaptive logics.
Talks by Aleks Knoks
Game theory is a branch of mathematics concerned with the analysis of strategic interaction among... more Game theory is a branch of mathematics concerned with the analysis of strategic interaction among agents in situations where the outcome of a participant's choice of action depends critically on the actions of other participants.
Conference Presentations by Aleks Knoks
The epistemic program in game theory aims at making explicit the assumptions that underlie the ba... more The epistemic program in game theory aims at making explicit the assumptions that underlie the basic concepts of the discipline. Thus far, it has not had much to say about the so-called ``trembling hand mistakes''. The goal of this paper is to fill in this lacuna. We argue that the idea of players that make and reason about mistakes fits naturally with the overall direction of the epistemic program. We present an extension of Robert Stalnaker's [3, 4] epistemic models of extensive games with simultaneous moves, in which the players can make trembling hand mistakes. In particular , this means that when a player observes an unexpected move, she has to figure out whether it is a result of a deliberate choice or simply a mistake. We show how our models shed new light on the relationship between backward and forward induction.
Uploads
Papers by Aleks Knoks
Drafts by Aleks Knoks
Talks by Aleks Knoks
Conference Presentations by Aleks Knoks