The fixed points of logic programs with herbrand base N

Herbrand Logic

Fixed Points in the Ambient Logic

We present an extension of the ambient logic with fixed points operators in the style of the μ-calculus. We give a simple syntactic condition for the equivalence between minimal and maximal fixpoint formulas and show how to subsume spatial analogues of the usual box and diamond operators.

Proof-theoretic aspects of modal logic with fixed points

An expansion of Basic Logic with fixed points

We introduce an expansion of Basic Logic (BL) with new connectives which express fixed points of continuous formulas, i.e. formulas of BL whose connectives are among {&,∨,∧}. The algebraic semantics of this logic is studied together with some of its subclasses corresponding to extensions of the above-mentioned expansion. The axiomatic extensions are proved to be standard complete.

On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs

Unlike monotone single-valued functions, multi-valued mappings may have none, one or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixed-points of multi-valued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these res...