Andreas Witzel

DEL planning and some tractable cases

We describe the planning problem within the framework of dynamic epistemic logic (DEL), considering the tree of sequences of events as the underlying structure. In general, the DEL planning problem is computationally difficult to solve. On the other hand, a great deal of fruitful technical advances have led to deep insights into the way DEL works, and these can be exploited in special cases. We present a few properties that will lead to considerable simplifications of the DEL planning problem and apply them in a toy example.

The synchronicity of dynamic epistemic logic

In a recent paper, van Benthem, Gerbrandy, Hoshi and Pacuit gave a natural translation of dynamic epistemic logic (DEL) into epistemic temporal logic (ETL) and proved a representation theorem, characterizing those ETL models that are translations of some DEL protocol; among the characterizing properties we also find synchronicity. In this paper, we argue that synchronicity is not an inherent property of DEL, but rather of the translation that van Benthem et al. used. We provide a different translation that produces asynchronous ETL models and discuss a minimal temporal extension of DEL that removes the ambiguities between the possible translations. This allows us a first attempt at assessing which of the epistemic-temporal properties are intrinsic to DEL and which are properties of the translation.

Cancer hybrid automata

This paper introduces Cancer Hybrid Automata (CHAs), a formalism to model the progression of cancers through discrete phenotypes. The classification of cancer progression using discrete states like stages and hallmarks has become common in the biology literature, but primarily as an organizing principle, and not as an executable formalism. The precise computational model developed here aims to exploit this untapped potential, namely, through automatic verification of progression models (e.g., consistency, causal connections, etc.), classification of unreachable or unstable states and computer-generated (individualized or universal) therapy plans. The paper builds on a phenomenological approach, and as such does not need to assume a model for the biochemistry of the underlying natural progression. Rather, it abstractly models transition timings between states as well as the effects of drugs and clinical tests, and thus allows formalization of temporal statements about the progression as well as notions of timed therapies. The model proposed here is ultimately based on hybrid automata, and we show how existing controller synthesis algorithms can be generalized to CHA models, so that therapies can be generated automatically. Throughout this paper we use cancer hallmarks to represent the discrete states through which cancer progresses, but other notions of discretely or continuously varying state formalisms could also be used to derive similar therapies.

Characterizing perfect recall using next-step temporal operators in S5 Epistemic Temporal Logic

We review the notion of perfect recall in the literature on interpreted systems, game theory and epistemic logic. In the context of Epistemic Temporal Logic (ETL), we give a (to our knowledge) novel frame condition for perfect recall. In contrast to existing characterizations, it is local in a sense which allows it to straightforwardly be translated into a defining formula in a language that only has next-step temporal operators. This frame condition also gives rise to a complete axiomatization of perfect recall in S5 ETL.

Towards Cancer Hybrid Automata

This paper introduces Cancer Hybrid Automata (CHAs), a formalism to model the progression of cancers through discrete phenotypes. The classification of cancer progression using discrete states like stages and hallmarks has become common in the biology literature, but primarily as an organizing principle, and not as an executable formalism. The precise computational model developed here aims to exploit this untapped potential, namely, through automatic verification of progression models (e.g., consistency, causal connections, etc.), classification of unreachable or unstable states and computer-generated (individualized or universal) therapy plans. The paper builds on a phenomenological approach, and as such does not need to assume a model for the biochemistry of the underlying natural progression. Rather, it abstractly models transition timings between states as well as the effects of drugs and clinical tests, and thus allows formalization of temporal statements about the progression as well as notions of timed therapies. The model proposed here is ultimately based on hybrid automata, and we show how existing controller synthesis algorithms can be generalized to CHA models, so that therapies can be generated automatically. Throughout this paper we use cancer hallmarks to represent the discrete states through which cancer progresses, but other notions of discretely or continuously varying state formalisms could also be used to derive similar therapies.

Power-law Null Model for Bystander Mutations in Cancer

In this paper we study Copy Number Variation (CNV) data. The underlying process generating CNV segments is generally assumed to be memory-less, giving rise to an exponential distribution of segment lengths. In this paper, we provide evidence from cancer patient data, which suggests that this generative model is too simplistic, and that segment lengths follow a power-law distribution instead. We conjecture a simple preferential attachment generative model that provides the basis for the observed power-law distribution. We then show how an existing statistical method for detecting cancer driver genes can be improved by incorporating the power-law distribution in the null model.

Choice and uncertainty in games

We consider an agent choosing between two acts A , B , whose outcomes are uncertain and depend on factors which the agent does not fully know. But for each pair of possible outcomes the agent does know how she would choose. Does the agent then have a way of choosing between the acts which will work at least some of the time?

Perfect recall of imperfect knowledge

Perfect recall, intuitively the ability to remember all past mental states, has been predominantly studied in the context of interpreted systems and game theory, which mostly consider S5 systems (of correct knowledge). More recently, the notion has become of interest to the epistemic logic community, where weaker systems are not unusual. Building upon recent work where we studied different definitions of perfect recall in Epistemic Temporal Logic (ETL), we argue that the intuitive motivations given there are still valid in such sub-S5 settings. However, definitions that were equivalent in S5 cease to be so without S5, so that these less restrictive settings allow for a more fine-grained comparison of the different definitions and their underlying intuitions.

Time constraints in mixed multi-unit combinatorial auctions

We extend the framework of mixed multi-unit combinatorial auctions, which deals with transformations of goods rather than only with atomic goods, by allowing time constraints in the bids offering these transformations. This way, bidders can express their scheduling preferences, while previously the auctioneer alone could decide the order of transformations.

Improving detection of driver genes: power-law null model of copy number variation in cancer

In this paper, we study Copy Number Variation (CNV) data. The underlying process generating CNV segments is generally assumed to be memory-less, giving rise to an exponential distribution of segment lengths. In this paper, we provide evidence from cancer patient data, which suggests that this generative model is too simplistic, and that segment lengths follow a power-law distribution instead. We conjecture a simple preferential attachment generative model that provides the basis for the observed power-law distribution. We then show how an existing statistical method for detecting cancer driver genes can be improved by incorporating the power-law distribution in the null model.