Concurrent information update in multi-agent systems: from Hintikka to Abramsky Games

Abramsky and Hintikka style games can be seen as representatives of the two main branches of game semantics. They both model interaction but each in a different manner. Hintikka games provide models of propositional interaction in terms of classical logic connectives such as ∨, ∧, →, and ¬. Abramsky games, on the other hand, model the interaction between programs that run in different parallel forms thus connecting them via linear logic connectives such as ⊗, (, ⊕ and &. I will discuss a possible application in which both of these approaches would co-exist, each at a different level, to provide a computational game semantics that also takes into account certain resources to reason about knowledge and update in multi-agent systems. Following Hintikka’s work in 1962 [9], modal and multi-modal epistemic logics have been extensively used to reason about knowledge of agents in multi-agent systems. In a multi-agent system, one crucial issue (apart from knowledge of each single agent) would be the change of the information state of agents due to the interaction between them. This issue was not addressed in existing epistemic logics. However, the interaction between programs and their effect on propositions was independently discussed in the work of V. Pratt in 1976 [11] following Dijkstra’s relational calculus for programs [5]. In these logics one could reason about the truth and falsity of propositions before and after running programs. Pratt’s work led to dynamic logic: a logic about program update. Although different forms of update where discussed in dynamic logic, the epistemic part was missing. One could not use dynamic logic to reason about information update. Baltag, Moss, and Solecki (BMS) [4] extended dynamic logic to epistemic propositions thus providing a full formalization of information update in 1999. They introduced the notion of an epistemic program that is, a program that changes the information state of agents. The significance of these programs is that they act not only on propositions of a propositional logic φ but also on epistemic propositions of a modal logic such as 2Aφ. Dynamic epistemic logic can be used to reason about what each agent knows before and after running an epistemic program.1 Hintikka games have been used by van Benthem to model knowledge in epistemic systems [12]. Abramsky games are considered as computational models of concurrent programs in a linear logic setting [1]. In such a setting programs that can run parallel to each other are considered as formulas of linear logic and thus as computational resources. A similar view of epistemic programs has been developed in Baltag, Coecke, It has to be noted that update was discussed in Fagin, Halpern et. al. in 1995 [8], but no formalization of epistemic programs was presented.