Inference

Argument Validity Check

Search the full table for a counterexample row.

logic-computation Every row is intentionally ordered and pinned to the lesson specification.

Example

Search the full table for a counterexample row.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\hlmath{\text{premises=0 R=0 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\hlmath{\text{premises=0 R=1 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\hlmath{\text{premises=0 R=0 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yesP=0 Q=1 R=1premises=0 R=1 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=1 R=1}&\hlmath{\text{premises=0 R=1 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yesP=0 Q=1 R=1premises=0 R=1 valid_row=yesP=1 Q=0 R=0premises=0 R=0 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=1 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=0 R=0}&\hlmath{\text{premises=0 R=0 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yesP=0 Q=1 R=1premises=0 R=1 valid_row=yesP=1 Q=0 R=0premises=0 R=0 valid_row=yesP=1 Q=0 R=1premises=0 R=1 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=1 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=1 Q=0 R=1}&\hlmath{\text{premises=0 R=1 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yesP=0 Q=1 R=1premises=0 R=1 valid_row=yesP=1 Q=0 R=0premises=0 R=0 valid_row=yesP=1 Q=0 R=1premises=0 R=1 valid_row=yesP=1 Q=1 R=0premises=0 R=0 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=1 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=1 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=1 R=0}&\hlmath{\text{premises=0 R=0 valid\_row=yes}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yesP=0 Q=1 R=1premises=0 R=1 valid_row=yesP=1 Q=0 R=0premises=0 R=0 valid_row=yesP=1 Q=0 R=1premises=0 R=1 valid_row=yesP=1 Q=1 R=0premises=0 R=0 valid_row=yesP=1 Q=1 R=1premises=1 R=1 valid_row=yes\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=1 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=1 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=1 Q=1 R=1}&\hlmath{\text{premises=1 R=1 valid\_row=yes}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

P=0 Q=0 R=0premises=0 R=0 valid_row=yesP=0 Q=0 R=1premises=0 R=1 valid_row=yesP=0 Q=1 R=0premises=0 R=0 valid_row=yesP=0 Q=1 R=1premises=0 R=1 valid_row=yesP=1 Q=0 R=0premises=0 R=0 valid_row=yesP=1 Q=0 R=1premises=0 R=1 valid_row=yesP=1 Q=1 R=0premises=0 R=0 valid_row=yesP=1 Q=1 R=1premises=1 R=1 valid_row=yesverdictvalid: no counterexample\begin{array}{c|c}\text{P=0 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=0 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=0 Q=1 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=0 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=1 Q=0 R=1}&\text{premises=0 R=1 valid\_row=yes}\\\text{P=1 Q=1 R=0}&\text{premises=0 R=0 valid\_row=yes}\\\text{P=1 Q=1 R=1}&\text{premises=1 R=1 valid\_row=yes}\\\text{verdict}&\hlmath{\text{valid: no counterexample}}\end{array}