# Publications in 2019

## 2019

- Confluence of the Chinese MonoidJörg Endrullis, and Jan Willem KlopIn: The Art of Modelling Computational Systems, pp. 206–220, Springer (2019)paper
# Summary

The Chinese monoid, related to Knuth’s Plactic monoid, is of great interest in algebraic combinatorics. Both are ternary monoids, generated by relations between words of three symbols. The relations are, for a totally ordered alphabet, if cba = cab = bca if a ≤ b ≤ c. In this note we establish confluence by tiling for the Chinese monoid, with the consequence that every two words u, v have extensions to a common word: ∀ u,v. ∃ x,y. ux = vy.

Our proof is given using decreasing diagrams, a method for obtaining confluence that is central in abstract rewriting theory. Decreasing diagrams may also be applicable to various related monoid presentations.

We conclude with some open questions for the monoids considered.

See research for an overview of my research on confluence.

# Bibtex

@inproceedings{confluence:chinese:monoid:2019, author = {Endrullis, J{\"{o}}rg and Klop, Jan Willem}, title = {{Confluence of the Chinese Monoid}}, booktitle = {The Art of Modelling Computational Systems}, series = {LNCS}, volume = {11760}, pages = {206--220}, publisher = {Springer}, year = {2019}, doi = {10.1007/978-3-030-31175-9\_12}, keywords = {rewriting,confluence}, type = {conference} }

# Digital Object Identifier

10.1007/978-3-030-31175-9_12

- Braids via Term RewritingJörg Endrullis, and Jan Willem KlopTheoretical Computer Science , 777 , pp. 260–295 (2019)paper
# Summary

We present a brief introduction to braids, in particular simple positive braids, with a double emphasis: first, we focus on term rewriting techniques, in particular, reduction diagrams and decreasing diagrams. The second focus is our employment of the colored braid notation next to the more familiar Artin notation. Whereas the latter is a relative, position dependent, notation, the former is an absolute notation that seems more suitable for term rewriting techniques such as symbol tracing. Artin's equations translate in this notation to simple word inversions. With these points of departure we treat several basic properties of positive braids, in particular related to the word problem, confluence property, projection equivalence, and the congruence property. In our introduction the beautiful diamond known as the permutohedron plays a decisive role.

# Bibtex

@article{rewriting:braids:2019, author = {Endrullis, J{\"{o}}rg and Klop, Jan Willem}, title = {Braids via term rewriting}, journal = {Theoretical Computer Science}, volume = {777}, pages = {260--295}, year = {2019}, doi = {10.1016/j.tcs.2018.12.006}, keywords = {rewriting,confluence}, type = {journal} }

# Digital Object Identifier

10.1016/j.tcs.2018.12.006

- Syllogistic Logic with "Most"Jörg Endrullis, and Lawrence S. MossMathematical Structures in Computer Science , 29 (6) , pp. 763–782 (2019)paper
# Summary

This paper presents a sound and complete proof system for the logical system whose sentences are of the form

- All X are Y,
- Some X are Y, and
- Most X are Y

This paper is an extended version of

*Syllogistic Logic with "Most"*presented at the International Workshop on Logic, Language, Information, and Computation (WoLLIC 2015).# Bibtex

@article{logic:most:2019, author = {Endrullis, J\"{o}rg and Moss, Lawrence S.}, title = {{Syllogistic Logic with "Most"}}, journal = {Mathematical Structures in Computer Science}, volume = {29}, number = {6}, pages = {763--782}, year = {2019}, doi = {10.1017/S0960129518000312}, keywords = {logic}, type = {journal} }

# Digital Object Identifier

10.1017/S0960129518000312