6 research outputs found
Cautious Belief and Iterated Admissibility
We define notions of cautiousness and cautious belief to provide epistemic
conditions for iterated admissibility in finite games. We show that iterated
admissibility characterizes the behavioral implications of "cautious
rationality and common cautious belief in cautious rationality" in a terminal
lexicographic type structure. For arbitrary type structures, the behavioral
implications of these epistemic assumptions are characterized by the solution
concept of self-admissible set (Brandenburger, Friedenberg and Keisler 2008).
We also show that analogous conclusions hold under alternative epistemic
assumptions, in particular if cautiousness is "transparent" to the players.
KEYWORDS: Epistemic game theory, iterated admissibility, weak dominance,
lexicographic probability systems. JEL: C72
Proceedings of the 11th Workshop on Nonmonotonic Reasoning
These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general
Intuitionism and logical revision.
The topic of this thesis is logical revision: should we revise the canons of classical
reasoning in favour of a weaker logic, such as intuitionistic logic? In the first part
of the thesis, I consider two metaphysical arguments against the classical Law of
Excluded Middle-arguments whose main premise is the metaphysical claim that
truth is knowable. I argue that the first argument, the Basic Revisionary Argument,
validates a parallel argument for a conclusion that is unwelcome to classicists
and intuitionists alike: that the dual of the Law of Excluded Middle, the Law of
Non-Contradiction, is either unknown, or both known and not known to be true.
As for the second argument, the Paradox of Knowability, I offer new reasons for
thinking that adopting intuitionistic logic does not go to the heart of the matter.
In the second part of the thesis, I motivate an inferentialist framework for
assessing competing logics-one on which the meaning of the logical vocabulary
is determined by the rules for its correct use. I defend the inferentialist account
of understanding from the contention that it is inadequate in principle, and I
offer reasons for thinking that the inferentialist approach to logic can help model theorists
and proof-theorists alike justify their logical choices. I then scrutinize the
main meaning-theoretic principles on which the inferentialist approach to logic
rests: the requirements of harmony and separability. I show that these principles
are motivated by the assumption that inference rules are complete, and that the
kind of completeness that is necessary for imposing separability is strictly stronger
than the completeness needed for requiring harmony. This allows me to reconcile
the inferentialist assumption that inference rules are complete with the inherent
incompleteness of higher-order logics-an apparent tension that has sometimes
been thought to undermine the entire inferentialist project.
I finally turn to the question whether the inferentialist framework is inhospitable
in principle to classical logical principles. I compare three different regimentations
of classical logic: two old, the multiple-conclusions and the bilateralist
ones, and one new. Each of them satisfies the requirements of harmony and separability,
but each of them also invokes structural principles that are not accepted
by the intuitionist logician. I offer reasons for dismissing multiple-conclusions
and bilateralist formalizations of logic, and I argue that we can nevertheless be
in harmony with classical logic, if we are prepared to adopt classical rules for
disjunction, and if we are willing to treat absurdity as a logical punctuation sign