# Publications on Logic

## 2019

- 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

## 2016

- Majority DigraphsTri Lai, Jörg Endrullis, and Lawrence S. MossProceedings of the American Mathematical Society , 144 (9) , pp. 3701–3715 (2016)paper
# Summary

A majority digraph is a finite simple digraph \( G = (V,\to) \) such that there exist finite sets \( A_v \) for the vertices \( v \in V \) with the following property: \( u \to v \) if and only if "more than half of the \( A_u \) are \( A_v \)". That is, \( u \to v \) if and only if \( | A_u \cap A_v | > \frac{1}{2} \cdot | A_u | \) . We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change to any real number \( \alpha \in (0, 1) \), we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions "most X are Y" and the standard connectives of propositional logic.

# Bibtex

@article{logic:most:graphs:2016, author = {Lai, Tri and Endrullis, J{\"o}rg and Moss, {Lawrence S.}}, title = {Majority digraphs}, journal = {Proceedings of the American Mathematical Society}, publisher = {American Mathematical Society}, volume = {144}, number = {9}, pages = {3701--3715}, year = {2016}, doi = {10.1090/proc/13038}, keywords = {logic}, type = {journal} }

# Digital Object Identifier

10.1090/proc/13038

## 2015

- Syllogistic Logic with "Most"Jörg Endrullis, and Lawrence S. MossIn: Proc. Int. Workshop on Logic, Language, Information, and Computation (WoLLIC 2015), pp. 124–139, Springer (2015)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

We have published an extended journal version of this paper in

*Mathematical Structures in Computer Science*, 2019.# Bibtex

@inproceedings{logic:most:2015, author = {Endrullis, J\"{o}rg and Moss, Lawrence S.}, title = {{Syllogistic Logic with "Most"}}, booktitle = {Proc.\ Int.\ Workshop on Logic, Language, Information, and Computation (WoLLIC~2015)}, volume = {9160}, pages = {124--139}, publisher = {Springer}, series = {LNCS}, year = {2015}, doi = {10.1007/978-3-662-47709-0\_10}, keywords = {logic}, type = {rewriting,conference} }

# Digital Object Identifier

10.1007/978-3-662-47709-0_10