Gradual Semantics for Logic-Based Bipolar Graphs Using T-(Co)norms

In this paper we consider a bipolar graph structure encoding conflicting knowledge with logic formulas. Gradual semantics provide a way to assign strength values in the unit interval to nodes (i.e. logical inference steps) in the bipolar graph. Here, we introduce a new class of semantics based on the notions of T-norms and T-conorms and show that they handle circular reasoning and satisfy desirable properties such as provability and rewriting.

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