Semantic tableaux for combined logical systems are usually constructed ad hoc and the problem of developing and applying more general methodologies for combining tableaux is yet to be systematically explored. In this talk I will address that problem and will outline some methodological approaches for combining tableaux for fibring, fusion, and products of logics. I will focus mainly on the case of fibring of tableaux and will discuss the questions of transfer of soundness, completeness, and termination from the components to the combined tableaux, both in general and in the context of some important special cases.

An important aspect of socially interacting rational agents are the strategic abilities of individual agents and groups (coalitions) of agents to guarantee the achievement of their desired goals, while acting and interacting within an entire society of agents. Several logical systems have been proposed for formalising and capturing such reasoning were introduced in the early 2000s, starting with the Coalition Logic (CL), the Alternating Time Temporal Logic (ATL), and some extensions of these. Coalition Logic provides a natural, but rather restricted perspective: the agents in the proponent coalition are viewed as acting in full cooperation with each other but in complete opposition to all agents outside of the coalition, which are thus treated as adversaries. The Alternating Time Temporal Logic extends Coalition Logic with temporal operators allowing for expressing long-term temporised goals. The strategic interaction in real societies is much more complex, usually involving various patterns combining cooperation and competition. To capture these, more expressive and versatile logical frameworks are needed. In this talk I will give a brief overview of some of these, and will then focus on the Logic of Coalitional Goal Assignments (LCGA), capturing reasoning about strategic abilities of the entire society to cooperate in order to ensure achievement of the societal goals, while simultaneously protecting the abilities of individuals and groups within the society to achieve their individual and group goals.