We consider equivalence relations and preorders complete for various levels of the arithmetical hierarchy under computable, component-wise reducibility. We show that implication in first order logic is a complete preorder for Σ1, the ≤m relation on EXPTIME sets for Σ2 and the embeddability of computable subgroups of (Q,+) for Σ3. In all cases, the symmetric fragment of the preorder is complete ...

In many types of planning algorithms distance heuristics play an important role. Most of the earlier works restrict to STRIPS operators, and their application to a more general language with disjunctivity and conditional effects first requires an exponential size reduction to STRIPS operators. I present direct formalizations of a number of distance heuristics for a general operator description ...

We describe a method for inverting Gentzen’s cut-elimination in classical first-order logic. Our algorithm is based on first computing a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize such a compression. Finally, a proof using these cut-formulas is constructed. This method allows an exponential compression of proof length. It can be appli...

The word problem for inverse monoids generated by a set Γ subject to relations of the form e = f , where e and f are both idempotents in the free inverse monoid generated by Γ , is investigated. It is shown that for every fixed monoid of this form the word problem can be solved in polynomial time which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presen...

BLOCKIN We BLOCKIN BLOCKIN have BLOCKIN BLOCKIN been asked by the editors of the Journal of Philosophical Logic to write a short comment on his most recent work, published in this issue, based in part on a referee report by one of us, that, unfortunately, did not reach Aldo in time.

We deene a class of modal logics LF by uniformly extending a class of modal logics L. Each logic L is characterised by a class of rst-order deenable frames, but the corresponding logic LF is sometimes characterised by classes of modal frames that are not rst-order deenable. The class LF includes provability logics with deep arithmeti-cal interpretations. Using Belnap's proof-theoretical framewo...

Assume that the problem P0 is not solvable in polynomial time. Let T be a first-order theory containing a sufficiently rich part of true arithmetic. We characterize T∪{ConT } as the minimal extension of T proving for some algorithm that it decides P0 as fast as any algorithm B with the property that T proves that B decides P0. Here, ConT claims the consistency of T . As a byproduct, we obtain a...

the objective of this study was to assess the potential of cadmium sulfide nanoparticles loaded onto activated carbon (cdsn-ac) for the removal of sunset yellow (sy) dye from aqueous solution. adsorption studies were conducted in a batch mode varying solution ph, contact time, initial dye concentration, cdsn-ac dose. in order to investigate the efficiency of sy adsorption on cdsn-ac, pseudo-fir...