## Propositional Logic: Examples

## Submit a Number of Premises

## Examples

simple examples | ||||
---|---|---|---|---|

examples with conjunctions and disjunctions | ||||

examples with implications and equivalences | ||||

complex examples | ||||

## Premises are Checked if They are Syntactically Well-Formed Formulas

The premises have to be syntactically well-formed formulas. Otherwise the program will not draw any conclusions. Instead it will indicate that at least one of the entered premises is not a well-formed formula.

Up to eight premises can be entered into the form. If you have more than eight premises, just connect some of them as a conjunction - (premise1 and premise2) - to reduce the number of premises to eight. When the submit button is pressed the PHP program draws all valid conclusions which can be drawn from the premises. The result is presented as a HTML table.

## Logically Valid Inferences are Drawn

The program draws all logically valid inferences from the premises which can be drawn. The drawing of some inferences requires a split into two lines of reasoning: If the formula '(A or B)' is true, then at least one of the formulas 'A' and 'B' is true. Hence the HTML table is split into two tables and both lines of reasoning are followed.

Every HTML table is one line of reasoning which can be followed given the premises. All HTML tables combined are all lines of reasoning which can be followed given the premises.

## Summary of the Result

The result is summarized in a final HTML table. In this final summarizing HTML table there is one row for every HTML table created in the step before. Every row shows for every variable of the premises if the line of reasoning makes the variable true (the variable occurs as a simple proposition in the HTML table), false (the variable occurs as a negated simple proposition in the HTML table), undetermined (the variable occurs neither as a simple proposition nor as a negated simple proposition in the HTML table), or a contradiction (the variable occurs both as a simple proposition and as a negated simple proposition in the HTML table).

If a row contains a contradiction, then the line of reasoning corresponding to this row is impossible. Otherwise it is possible.

If this final summarizing HTML table contains at least one row which says that its line of reasoning is possible, then the premises are compatible. Otherwise the premises are incompatible.