Publications on Logic

2019

Syllogistic Logic with "Most"
Jörg Endrullis, and Lawrence S. Moss
Mathematical Structures in Computer Science , 29 (6) , pp. 763–782 (2019)
summary paper bib doi
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
where we interpret these sentences on finite models, with the meaning of `most' being `strictly more than half'. Our proof system is syllogistic; there are no individual variables.

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 Digraphs
Tri Lai, Jörg Endrullis, and Lawrence S. Moss
Proceedings of the American Mathematical Society , 144 (9) , pp. 3701–3715 (2016)
summary paper bib doi

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. Moss
In: Proc. Int. Workshop on Logic, Language, Information, and Computation (WoLLIC 2015), pp. 124–139, Springer (2015)
summary paper bib doi
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
where we interpret these sentences on finite models, with the meaning of `most' being `strictly more than half'. Our proof system is syllogistic; there are no individual variables.

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
```