Decision mode vs argument mode: meaning and examples

Decision mode is the way of working in which a model has named outputs, each a formula over the inputs, and the checks ask about those outputs. Argument mode instead has premises and one conclusion, and the checks ask whether the conclusion follows.

The two modes are two readings of the same truth table. In decision mode each formula is a rule, allow, discount, alarm, computed on every row, and the natural questions are whether it can fire, whether it always fires, whether two rules agree, and which inputs it depends on. In argument mode the formulas are premises plus a conclusion, and the single question is validity: is there a row where every premise holds and the conclusion fails. Assumptions belong to decision mode, premises to argument mode.

The artefact on this page is a decision model with one output, allow = (member OR invited) AND NOT banned. Its 8-row table is true on rows 2, 4 and 6. The checks are the decision-mode set: the tautology check is violated with the counterexample member = FALSE, invited = FALSE, banned = FALSE, so the rule does not always grant entry; the contradiction check is violated and the satisfiable check holds, both with the witness member = FALSE, invited = TRUE, banned = FALSE, so it can. In argument mode the formula would need a conclusion to test.

Decision mode is the mode for business rules, access policies, feature flags and circuits, where the outputs are the point; argument mode is for logic exercises and for policies written as “from these facts it follows that”. Choosing wrongly is harmless but confusing, since a premise and an output are checked differently. The term is confused with a decision table (a layout, not a mode) and with the decision in coverage criteria, which is one Boolean expression in code.

Example

allow := (member OR invited) AND NOT banned · output

Exact checks

Always true (tautology)? No Counterexample: member = F, invited = F, banned = F · Exhaustively checked and solver cross-checked · 1 rows

Always false (contradiction)? No Counterexample: member = F, invited = T, banned = F · Exhaustively checked and solver cross-checked · 3 rows

Can be true? Yes Example assignment: member = F, invited = T, banned = F · Exhaustively checked and solver cross-checked · 3 rows

Truth table (8 rows)

Decision mode vs argument mode: meaning and examples
#	member	invited	banned	allow
0	FALSE	FALSE	FALSE	FALSE
1	FALSE	FALSE	TRUE	FALSE
2	FALSE	TRUE	FALSE	TRUE
3	FALSE	TRUE	TRUE	FALSE
4	TRUE	FALSE	FALSE	TRUE
5	TRUE	FALSE	TRUE	FALSE
6	TRUE	TRUE	FALSE	TRUE
7	TRUE	TRUE	TRUE	FALSE

Plain-language reading

Beginnerallow is true exactly when both of the following hold:
1. at least one of member or invited is true (both may be true)
2. banned is false
In every other case, allow is false.
About the operators:
- AND is true only when all of its parts are true.
- OR is inclusive: it is true when at least one part is true, including when several are.
- NOT reverses a value: true becomes false and false becomes true.

Intermediateallow is true exactly when both of the following hold:
1. at least one of member or invited is true (both may be true)
2. banned is false
In every other case, allow is false.

Advancedallow is true exactly when both of the following hold [conjunction ∧]:
1. at least one of member or invited is true (both may be true) [inclusive disjunction ∨]
2. banned is false [negation ¬]
In every other case, allow is false.
Formal notation: (member ∨ invited) ∧ ¬banned

The common slip

Putting a conclusion into decision mode as just another output. The engine then reports its tautology and satisfiability, not whether it follows from the others. To test that the conclusion follows, switch to argument mode, where the premises constrain which rows count.

Questions

Can one model have several outputs?

Yes, in decision mode: the full adder on the combinational-logic page has sum and carry_out over the same inputs, each with its own column and checks. Argument mode has exactly one conclusion.

Glossary

Generated from the Tangibool engine, semantics tangibool-semantics/1, engine 1.0.0, build 2026-11-07. Every table, map, simplification and verdict on these pages was computed by the Tangibool engine when the site was built, and every claim was re-checked by the same exact checker the app uses. Limits are stated where they apply. © 2026 Foreranger LTD.