Notes-computational-theory-evidence-based-reasoning

Tecuci et. al. have made a serious attempt to develop a general approach to evidence-based reasoning based on Schum’s work. These notes are on their latest work [@tecuci:2019:computational].

As a preface, my proposed project has leaned towards starting such an investigation with Peircean semiotics, formalized with category theory. So I have a pre-exisiting bias. But Tecuci’s previous work has taken Peirce seriously, in particular Peirce’s abduction-deduction-induction logic of science. Although Bellucci shows that Peirce revised this order in his later work on speculative grammar [@bellucci:2018:peirce], we’ll have to await Bellucci’s volumes on Peirce’s speculative rhetoric to see if there was a corresponding impact on his theory of inquiry.

Tecuci begins with identifying abduction with possibility, deduction with necessity and induction with probability. Now one approach to categorical probability is through Lawvere’s space-quantity adjunction, with total probability as an extrinsic quantity and probability density as an intrinsic quantity. Lawvere’s Kan quantifiers form an adjoint pair that generalize first-order logical quantifiers [@lawvere:1986:taking].

Adjoint triple from Nlab: An adjoint triple of functors gives rise to an adjoint monad/comonad pair; it is the latter that gives rise to the possibility/necessity modalities. The link between the two adjunctions is an adjunction; an adjoint triple is also an adjuction between adjunctions.

The notion of a general theory of knowledge, which must underly any theory of inquiry (as knowledge change), or what Peirce called ‘logical critic’, has been approached in category theory by Patterson, who proposed a variety of categorical knowledge representation formalisms based on different categorical notions. Patterson’s work used the bicategory of relations, but points to a larger framework. As an aside, could the monoidal functor approach as a box developed by Meilles be applied as a knowledge representation framework a la the existential graphs.

An interruption: Nicholas Rescher wrote an introductory book on epistemology and two books on value theory.