Towards Partial Reasoning

Krzysztof Zbigniew Nowak

This paper presents a framework for reasoning with partial information provided by multiple agents. On the semantic side, there are partial objects corresponding to equivalence classes of indiscernible objects. Sets of partial objects form partial worlds. On the syntactic side, agents describe their partial worlds, and their description sets are taken as sets of axioms for formal systems with intuitive rules of inference. Given a formal system, its set of theorems forms a consistent partial theory. The set of all theories is equipped with an information ordering and forms a lattice. The lattice structure allows to visualise how theories, and agents, support or contradict each other. The set of description sets provided by agents determines a set of theories believed by the agents, and this set gives rise to a sub-lattice of the set of all theories. The framework is appropriate for dealing with information provided by multiple sources of information, with emphasis on partial and contradictory information.

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