Lower semilattice-ordered residuated semigroups and substructural logics

We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions (terms, sequents, equations, quasi-equations) in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics

Traces within traces : holes, pits and galleries in walls and filling of insect trace fossils in paleosols

Fossil insect nests with constructed walls (ichnogenera Uruguay ROSELLI 1938, Palmiraichnus ROSELLI 1987, Rosellichnus GENISE and BOWN 1996), as well as fossil brood masses from dung beetles (Monesichnus ROSELLI 1987) often display pits or galleries made by inquilines, parasitoids, cleptoparasites and scavengers, which develop and/or feed inside them. Some of these "traces within traces" can be distinguished, using morphologic criteria, as separate ichnotaxa. Tombownichnus n. igen. is represented by circular to subcircular holes or paraboloid external pits occurring in discrete walls of chambers made of agglutinated soil material. T. plenus n. isp. consists of a complete perforation, mostly cylindrical in longitudinal section, which pierces whole thickness of the cell wall. Tombownichnus parabolicus n. isp. includes incomplete perforations, i.e. pits, parabolic, conic or subcylindrical in longitudinal section, on the external surface of the chamber wall. Lazaichnus fistulosus n. igen., n. isp. is composed of circular to subcircular holes occurring in constructed walls of chambers made of agglutinated soil material, which are connected to an internal gallery in their infillings. The trace fossils described herein may be the first formal records of this hitherto neglected but promising field of ichnologic research

Traces within traces : holes, pits and galleries in walls and filling of insect trace fossils in paleosols

Fossil insect nests with constructed walls (ichnogenera Uruguay ROSELLI 1938, Palmiraichnus ROSELLI 1987, Rosellichnus GENISE and BOWN 1996), as well as fossil brood masses from dung beetles (Monesichnus ROSELLI 1987) often display pits or galleries made by inquilines, parasitoids, cleptoparasites and scavengers, which develop and/or feed inside them. Some of these "traces within traces" can be distinguished, using morphologic criteria, as separate ichnotaxa. Tombownichnus n. igen. is represented by circular to subcircular holes or paraboloid external pits occurring in discrete walls of chambers made of agglutinated soil material. T. plenus n. isp. consists of a complete perforation, mostly cylindrical in longitudinal section, which pierces whole thickness of the cell wall. Tombownichnus parabolicus n. isp. includes incomplete perforations, i.e. pits, parabolic, conic or subcylindrical in longitudinal section, on the external surface of the chamber wall. Lazaichnus fistulosus n. igen., n. isp. is composed of circular to subcircular holes occurring in constructed walls of chambers made of agglutinated soil material, which are connected to an internal gallery in their infillings. The trace fossils described herein may be the first formal records of this hitherto neglected but promising field of ichnologic research

Residuated Kleene algebras

We show that there is no finitely axiomatizable class of algebras that would serve as an analogue to Kozen’s class of Kleene algebras if we include the residuals of composition in the similarity type of relation algebras