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Proving that one language is more succinct than another becomes harder when the underlying semantics is stronger. We propose to use Formula-Size Games (as put forward by Adler and Immerman, 2003), games that are played on two sets of models , and that directly link the length of play with the size of the formula. Using FSGs, we prove three succinctness… (More)

- Petar Iliev
- 2013

We present two families of exponential lower bounds on the size of modal formulae and use them to establish the following succinctness results. We show that the logic of contingency (ConML) is exponentially more succinct than basic modal logic (ML). We strengthen the known proofs that the so-called public announcement logic (PAL) in a signature containing… (More)

The last decade has been witness to a rapid growth of interest in logics intended to support reasoning about the interactions between knowledge and action. Typically, logics combining dynamic and epistemic components contain ontic actions (which change the state of the world, e.g., switching a light on) or epistemic actions (which affect the information… (More)

In the study of knowledge representation formalisms, there is a current interest in the question of how different formal languages compare in their ability to compactly express semantic properties. Recently, French et al. [9] have shown that modal logics with a modality for public announcement, for everybody knows, and for somebody knows are all… (More)

The growing number of logics has lead to the question: How do we compare two formalisms? A natural answer is: We can compare their expressive power and computational properties. There is, however, another way of comparing logics that has attracted attention recently, namely in terms of representational succinctness, i.e., we can ask whether one of the… (More)

We introduce and study the notion of a Public Environment: a system in which a publicly known program is executed in an environment that is partially observable to agents in the system. Although agents do not directly have access to all variables in the system, they may come to know the values of unobserved variables because they know how the program is… (More)

The natural modal logic corresponding to Pawlak's approximation spaces is S5, based on the box modality [R]A (and the diamond modality RA = ¬[R]¬A), where R is the corresponding indiscernibility relation of the approximation space S = (W, R). However the expressive power of S5 is too weak and, for instance, we cannot express that the space S has exactly n… (More)

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