Preliminaries Alternating-time temporal logic (ATL) [1] is designed to specify collaborative as well as adversarial interaction between different components of a distributed system. Checking the validity of an alternating-time property in an explicit model is cheap: linear in the size of the formula and the model. Alternating transition systems (ATS) are used to model reactive components and th...

We propose a logic for reasoning about (multi-agent) epistemic probability models, and for epistemic probabilistic model checking. Epistemic probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds, together with function from worlds to positive rationals (a lottery). The difference with the usual approach is that probability is linked to know...

We consider the family of Φ-Subset problems, where the input consists of an instance I of size N over a universe UI of size n and the task is to check whether the universe contains a subset with property Φ (e.g., Φ could be the property of being a feedback vertex set for the input graph of size at most k). Our main tool is a simple randomized algorithm which solves Φ-Subset in time (1 + b − 1 c...

Keywords: restricted ω-rule, not-semi-decidable, limits of proof verification The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. 1 This wisdom presumably does hold for conventional proof systems such as first-order logic with a standard proof calc...

Equilibrium checking is concerned with establishing whether a given temporal logic formula φ is satisfied in some or all equilibrium computations of a multi-agent system – that is, whether the system will exhibit the behaviour φ under the assumption that agents within the system act rationally in pursuit of their preferences. After motivating and introducing the framework of equilibrium checkin...

In the plethora of fragments of Halpern and Shoham’s modal logic of time intervals (HS), the logic AB of Allen’s relations Meets and Started-by is at a central position. Statements that may be true at certain intervals, but at no sub-interval of them, such as accomplishments, as well as metric constraints about the length of intervals, that force, for instance, an interval to be at least (resp....