Title: Variations on Weakly Aggregative Modal Logic

Speaker: Yifeng Ding (PKU)

Time: 15:10 ~ 18:00 (Oct. 4)

Location: Room 404, No.3 Teaching Building

Abstract:

When axiomatizing the minimal normal modal logic K, instead of the K axiom, one can also do with the aggregation axiom that states that box p and box q implies box (p and q). That is, propositions in the boxed context can ba 'aggregated'. Weakly aggregative modal logics weaken this aggregation axiom in a seemingly cryptic way: instead of aggregating two propositions into their conjunction, in the first non-normal weakly aggregative modal logic, we can aggregate three propositions into the disjunction of their pairwise conjunction; that is, from box p, box q, and box r, we can infer box ((p and q) or (p and r) or (q and r)). While less prominent in the modal logic literature, weakly aggregative modal logic is actually a unifying theme behind many apparently different topics such as polyadic modal logic, paraconsistent reasoning, modal logic for hypergraphs, frame-of-mind models for non-omniscient knowledge representation, and the 'someone knows' concept for group knowledge. To illustrate the above three-way weak aggregation reasoning, take box to mean 'true in all but at most one possible world', and then the reasoning is valid. Our talk will start with some semantic discussion of weakly aggregative modal logics and then connect it to more applied topics such as 'someone knows'.