# Non-commutative propositional logic with short-circuited biconditional and NAND

@article{Papuc2022NoncommutativePL, title={Non-commutative propositional logic with short-circuited biconditional and NAND}, author={Dalia Papuc and Alban Ponse}, journal={ArXiv}, year={2022}, volume={abs/2203.09321} }

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit evaluation is widely used, with left-sequential conjunction and disjunction as primitive connectives. We consider left-sequential, non-commutative propositional logic, also known as MSCL (memorising short-circuit logic), and start from a previously published…

## References

SHOWING 1-10 OF 17 REFERENCES

### Non-commutative propositional logic with short-circuit evaluation

- Computer ScienceJ. Appl. Non Class. Logics
- 2021

This work considers the case that atoms can also evaluate to the truth value 'undefined' and presents evaluation trees as an intuitive semantics and provides complete independent equational axiomatisations.

### Evaluation trees for proposition algebra. https://arxiv.org/abs/1504.08321v3 [cs.LO

- 2015

### Short-circuit logic. https://arxiv.org/abs/1010.3674v4 [cs.LO,math.LO

- (Last version (v4):
- 2013

### An independent axiomatisation for free short-circuit logic

- PhilosophyJ. Appl. Non Class. Logics
- 2018

This work provides a simple semantics for free short-circuit logic (SCL) and an independent axiomatisation and discusses evaluation strategies, some other SCLs, and side effects.

### Logical systems with left-sequential versions of NAND and XOR

- Thesis MSc Logic (June 25th,
- 2020

### Introduction to mathematical logic

- PhilosophyUniversitext
- 1973

This book discusses the semantics of Predicate Logic, and some of theorems of A. Robinson, Craig and Beth's treatment of Peano's Axiom System.

### A set of five independent postulates for Boolean algebras, with application to logical constants

- Mathematics
- 1913

Postulate-sets for determining the class of Boolean algebrasf have been given by Schröder,^ Whttehead,§ and Huntington.|| Schroder's set of ten postulates assumes—in addition to an undefined class K,…

### Decision Trees and Diagrams

- Computer ScienceCSUR
- 1982

In this tutorial survey a common framework of defimtmns and notation is established, the contributions from the main fields of apphcatmn are reviewed, recent results and extensions are presented, and areas of ongoing and future research are discussed.