# Problem with redefining operators for propositional logic
**URL:** https://swi-prolog.discourse.group/t/problem-with-redefining-operators-for-propositional-logic/2555
**Category:** Help!
**Created:** [June 24, 2020, 7:02am UTC](https://swi-prolog.discourse.group/t/problem-with-redefining-operators-for-propositional-logic/2555 "2020-06-24T07:02:57Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@carstenheisterkamp](https://swi-prolog.discourse.group/u/carstenheisterkamp)
#### Post date: [June 24, 2020, 7:02am UTC](https://swi-prolog.discourse.group/t/problem-with-redefining-operators-for-propositional-logic/2555/1 "2020-06-24T07:02:57Z")
Hi, teaching myself prolog I found an [interesting article](http://icebergsystems.ca/articles/propositional-logic-in-prolog) about how to rewrite Prolog operators to represent propositional logic, so that you can formulate propositions like:
`P = t('A is a knight'),Q = t('B is a knight'), P <=> ~P ^ Q.`
I created this [notbook on swish](https://swish.swi-prolog.org/p/XNRWNgWg.pl) with the complete code.
It redefines the operators two times and aliases them. But the `not` alias` ~`, the `implies` and the `equiv` alias don´t work and I get an “operator expected” error in swish and swipl. The code looks ok, but what am I missing, or misunderstanding?
```
% infix syntax for logical connectives
:- op(400,xf,not).
:- op(500,xfx,and).
:- op(500,xfx,or).
:- op(600,xfx,implies).
:- op(600,xfx,equiv).
% logical operators for the connectives
:- op(400,xf,~).
:- op(500,xfx,^).
:- op(500,xfx,v).
:- op(600,xfx,=>).
:- op(600,xfx,<=>).
% aliases of the connectives
~P :- not P.
P ^ Q :- P and Q.
P v Q :- P or Q.
P => Q :- P implies Q.
P <=> Q :- P equiv Q.
```
---
### Author:  [@bwat](https://swi-prolog.discourse.group/u/bwat)
#### Post date: [June 24, 2020, 8:27am UTC](https://swi-prolog.discourse.group/t/problem-with-redefining-operators-for-propositional-logic/2555/2 "2020-06-24T08:27:32Z")
Try fy instead of xf. What I use when I code propositional logic routines:
```prolog
%%%
%%% 2.1 The syntax of propositional logic
%%%
%%% I use the built in parser and change/augment the Prolog operators to handle
%%% propositional logic.
%%%
:-op(0, fy, ~).
:-op(200, fy, ~). % Negation
:-op(0, yfx, (/\)).
:-op(0, xfy, (/\)).
:-op(400, xfy, (/\)). % Conjunction (not ISO associativity which \
is yfx)
:-op(0, yfx, (\/)).
:-op(0, xfy, (\/)).
:-op(500, xfy, (\/)). % Disjunction (not ISO associativity which \
is yfx)
:-op(0, xfy, ==>).
:-op(600, xfy, ==>). % Implication
:-op(0, xfy, <=>).
:-op(700, xfy, <=>). % Equivalence
```
Top tip: to test your understanding of operator precedence try this query
```prolog
read(X), write_canonical(X).
```
and give it some typical input and make sure it works as you think it should. Here’s an example from the manual of my Prolog system:
```prolog
| ?- op(200, xfx, @).
% yes
| ?- op(300, xfx, &).
% yes
| ?- write_canonical(a @ b & c), nl.
&(@(a,b),c)
```