Nik Swoboda - Observation: Understanding how information can be extracted from diagrams.

A great deal of the information that we gather each day comes from diagrammatic sources. In fact, we commonly make many important decisions based upon information gathered from maps, graphs and the like. Recently, a lot of work has been done to establish very precise mathematical systems for reasoning with diagrams. In this presentation I will start with a short introduction to reasoning with diagrams focusing specifically on heterogeneous proofs. Here I will take a heterogeneous proof to be a proof which uses both diagrams and sentences in an essential way. In such proofs there are two important rules, one for extracting information from the diagram into the sentential language and one extracting information from the sentences and adding it to a diagram. I will call the process of extracting information from the diagram observation and focus the remainder of the discussion on this notion. I will give one interpretation of what it means to observe something from a diagram and based upon this discussion I will give an example of how this notion of observation can be mathematically defined, using Barwise/Seligman Information Theory, for Euler/Venn diagrams.