27,924 research outputs found
Agent-update Models
In dynamic epistemic logic (Van Ditmarsch et al., 2008) it is customary to
use an action frame (Baltag and Moss, 2004; Baltag et al., 1998) to describe
different views of a single action. In this article, action frames are extended
to add or remove agents, we call these agent-update frames. This can be done
selectively so that only some specified agents get information of the update,
which can be used to model several interesting examples such as private update
and deception, studied earlier by Baltag and Moss (2004); Sakama (2015); Van
Ditmarsch et al. (2012). The product update of a Kripke model by an action
frame is an abbreviated way of describing the transformed Kripke model which is
the result of performing the action. This is substantially extended to a
sum-product update of a Kripke model by an agent-update frame in the new
setting. These ideas are applied to an AI problem of modelling a story. We show
that dynamic epistemic logics, with update modalities now based on agent-update
frames, continue to have sound and complete proof systems. Decision procedures
for model checking and satisfiability have expected complexity. A sublanguage
is shown to have polynomial space algorithms
Cheryl's Birthday
We present four logic puzzles and after that their solutions. Joseph Yeo
designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for
'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind
Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the
puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other
knowledge puzzles, and that can also be found on the webpage
http://personal.us.es/hvd/lightbulb.html dedicated to the book.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Exploiting Asymmetry in Logic Puzzles: Using ZDDs for Symbolic Model Checking Dynamic Epistemic Logic
Binary decision diagrams (BDDs) are widely used to mitigate the
state-explosion problem in model checking. A variation of BDDs are
Zero-suppressed Decision Diagrams (ZDDs) which omit variables that must be
false, instead of omitting variables that do not matter. We use ZDDs to
symbolically encode Kripke models used in Dynamic Epistemic Logic, a framework
to reason about knowledge and information dynamics in multi-agent systems. We
compare the memory usage of different ZDD variants for three well-known
examples from the literature: the Muddy Children, the Sum and Product puzzle
and the Dining Cryptographers. Our implementation is based on the existing
model checker SMCDEL and the CUDD library. Our results show that replacing BDDs
with the right variant of ZDDs can significantly reduce memory usage. This
suggests that ZDDs are a useful tool for model checking multi-agent systems.Comment: In Proceedings TARK 2023, arXiv:2307.0400
Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism
This essay examines the philosophical significance of -logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of -logical validity can then be countenanced within a coalgebraic logic, and -logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of -logical validity correspond to those of second-order logical consequence, -logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets
Belief Revision with Uncertain Inputs in the Possibilistic Setting
This paper discusses belief revision under uncertain inputs in the framework
of possibility theory. Revision can be based on two possible definitions of the
conditioning operation, one based on min operator which requires a purely
ordinal scale only, and another based on product, for which a richer structure
is needed, and which is a particular case of Dempster's rule of conditioning.
Besides, revision under uncertain inputs can be understood in two different
ways depending on whether the input is viewed, or not, as a constraint to
enforce. Moreover, it is shown that M.A. Williams' transmutations, originally
defined in the setting of Spohn's functions, can be captured in this framework,
as well as Boutilier's natural revision.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in
Artificial Intelligence (UAI1996
Tools for Thought: The Case of Mathematics
The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced
- …