A note on a generalization of the muddy children puzzle

ABSTRACT We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifiers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specific informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety)

Symbolic Model Checking for Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, existing DEL implementations are ad-hoc, so we do not know how the framework really performs. For this purpose, we want to hook up with the best available model-checking and SAT techniques in computational logic. We do this by first providing a bridge: a new faithful representation of DEL models as so-called knowledge structures that allow for symbolic model checking. Next, we show that we can now solve well-known benchmark problems in epistemic scenarios much faster than with existing DEL methods. Finally, we show that our method is not just a matter of implementation, but that it raises significant issues about logical representation and update

New Directions in Model Checking Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, its existing implementations are based on explicit model checking which can only deal with small models, so we do not know how DEL performs for larger and real-world problems. For temporal logics, in contrast, symbolic model checking has been developed and successfully applied, for example in protocol and hardware verification. Symbolic model checkers for temporal logics are very efficient and can deal with very large models. In this thesis we build a bridge: new faithful representations of DEL models as so-called knowledge and belief structures that allow for symbolic model checking. For complex epistemic and factual change we introduce transformers, a symbolic replacement for action models. Besides a detailed explanation of the theory, we present SMCDEL: a Haskell implementation of symbolic model checking for DEL using Binary Decision Diagrams. Our new methods can solve well-known benchmark problems in epistemic scenarios much faster than existing methods for DEL. We also compare its performance to to existing model checkers for temporal logics and show that DEL can compete with established frameworks. We zoom in on two specific variants of DEL for concrete applications. First, we introduce Public Inspection Logic, a new framework for the knowledge of variables and its dynamics. Second, we study the dynamic gossip problem and how it can be analyzed with epistemic logic. We show that existing gossip protocols can be improved, but that no perfect strengthening of "Learn New Secrets" exists

The principle of analyticity of logic : a philosophical and formal Perspective

The subject of the present work is the principle of analyticity of logic. In order for the question \u2018Is logic analytic?\u2019 to make sense and before trying to \ufb01nd an answer to this problem, it is obviously necessary to specify two preliminary issues, namely, the meaning of the term \u2018analytic\u2019 and the meaning of the term \u2018logic\u2019. The former issue is somehow justi\ufb01ed and expected: after all, analyticity represents one of the philosophical concepts par excellence and, as such, it has been at the core of a lively debate throughout the history of the discipline. But, despite possible appearances to the contrary, the second issue is probably more decisive than the former in determining the answer to the initial question: both the contents and the philosophical conceptions of logic play a fundamental role in the study of the epistemological status of this discipline. We could even say that the clari\ufb01cation of the concepts of analyticity and of logic constitutes in itself the decision on the analyticity of logic. This thesis studies the principle of analyticity of logic through two di\ufb00erent, but related, methodologies, which individuate the two main parts of the work: the former o\ufb00ers a historical and philosophical reconstruction of the problem; the latter proposes two formal characterizations of the analytic-synthetic distinction. The reconstruction of the \ufb01rst part does not presume to be exhaustive and is restricted to the theories of the following philosophers: Kant, Bolzano, Frege and Hintikka. The material has been chosen according to the following criteria. First, this work aims at showing the \u2018historical\u2019 nature of the principle of analyticity of logic, which has a certain genealogy and a precise starting point. Although after the Vienna Circle this tenet has been taken for granted, there are many and signi\ufb01cant conceptions that criticize it. Theories holding that logic is either not analytic or synthetic are the main characters of our reconstruction. This explains, for example, why we have dedicated great attention to Bolzano, while leaving little margin to the logical empiricist movement, despite the fact that analyticity is probably more fundamental for the latter\u2019s thought than for the former\u2019s philosophical construction. As a result of this choice, theories of meaning and their connection to analyticity are completely overlooked, since they belong to the logical empiricists\u2019 interpretation of the analytic-synthetic distinction. In other words, the principle of analyticity of logic and the philosophers arguing for it are taken as a critical target, but the true focus is on the varieties of reactions against them. [...

A note on a generalization of the Muddy Children Puzzle

We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifiers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specific informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety)