Paraconsistent Foundations for Probabilistic Reasoning, Programming and
  Concept Formation
  It is argued that 4-valued paraconsistent truth values (called here "p-bits")
can serve as a conceptual, mathematical and practical foundation for highly
AI-relevant forms of probabilistic logic and probabilistic programming and
concept formation.
  First it is shown that appropriate averaging-across-situations and
renormalization of 4-valued p-bits operating in accordance with Constructible
Duality (CD) logic yields PLN (Probabilistic Logic Networks)
strength-and-confidence truth values. Then variations on the Curry-Howard
correspondence are used to map these paraconsistent and probabilistic logics
into probabilistic types suitable for use within dependent type based
programming languages.
  Zach Weber's paraconsistent analysis of the sorites paradox is extended to
form a paraconsistent / probabilistic / fuzzy analysis of concept boundaries;
and a paraconsistent version of concept formation via Formal Concept Analysis
is presented, building on a definition of fuzzy property-value degrees in terms
of relative entropy on paraconsistent probability distributions.
  These general points are fleshed out via reference to the realization of
probabilistic reasoning and programming and concept formation in the OpenCog
AGI framework which is centered on collaborative multi-algorithm updating of a
common knowledge metagraph.
