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Approximation Fixpoint Theory as a General Algebraic Theory of Constructive Knowledge (FWOAL990)

Approximation Fixpoint Theory (AFT) is an algebraic fixpoint theory
nonmonotone operators. It was founded in order to unify semantics
of various non-monontic logics, in particular default logic (DL),
autoepistemic logic (AEL), and logic programming (LP).
Using AFT, one can obtain a family of semantics for any of these
logics by defining (only) a semantic operator: an operator that maps
interpretations to interpretations given a logic theory.
The high level of abstraction and mathematical elegance of AFT
make it a suitable tool for studying the underlying principles present
in all such logics .

Following its original succes in unifying DL, AEL and LP, AFT has
been applied to numerous other domains, prompting several
extensions of the original theory.
AFT has greatly simplified the characterisation and subsequent study
of semantics and constructive processes in the different domains to
which it has been applied.

The goal of this project is to lift AFT into a general theory for
constructive knowledge. By doing so, we will bring the benefits the
theory offers (such as the fact that it unifies domains, that
stratification results are freely available, ... ) to a wide range of
application areas within computer science
Date:1 Jan 2021 →  Today
Keywords:Approximation fixpoint theory, constructive knowledge
Disciplines:Computational logic and formal languages, Knowledge representation and reasoning, Mathematical logic and foundations, Order, lattices, ordered algebraic structures