Abstract
In this paper, we propose an additional application area of the subset space semantics of modal logic in terms of cooperating agents. While the original conception reflects both the knowledge acquisition process and the accompanying topological effect for a single agent, we show how a slight extension of that system can be utilized for modeling agents which, in a strict sense, cooperate for knowledge. In so doing, the agents will come in by means of so-called effort functions. These functions shall represent those of the agents’ actions which are targeted at more knowledge of the whole group. Our investigations result in a particular multi-agent version of the well-known logic of subset spaces, which allows us to reason about qualitative aspects of cooperation like the dominance of a joint commitment over any individual effort. On the technical side, a soundness and completeness theorem for one of the logics arising from that will be proved.
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Notes
- 1.
This is in accordance with the general setting in the context of subset spaces.
- 2.
The part this operator plays in the novel system will become apparent later.
- 3.
If the effort functions shall depend on knowledge states alone, then topological nexttime logic, see [9], would enter the field. This would lead to a somewhat more complicated but related system.
- 4.
In other words, the schema \((p \rightarrow \mathsf {C}_i p)\wedge (\mathsf {C}_i p\rightarrow p)\) is \(\mathsf {CALSS}_n\)-derivable.
- 5.
This point of view is derived by analogy with sequencing from the theory of parallel programming.
- 6.
One or another proof of such a kind can be found in the literature; see, as regards a fully completed version for \(\mathsf {LSS}\), [4]. Note that the special circumstances of each individual case require an appropriate adjustment, which is most often non-trivial.
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Heinemann, B. (2016). A Subset Space Perspective on Agents Cooperating for Knowledge. In: Lehner, F., Fteimi, N. (eds) Knowledge Science, Engineering and Management. KSEM 2016. Lecture Notes in Computer Science(), vol 9983. Springer, Cham. https://doi.org/10.1007/978-3-319-47650-6_40
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