Example Data Table
These examples show common construction reasoning patterns.
| Premises |
Conclusion |
Main rule |
Expected result |
P -> Q, P |
Q |
Modus ponens |
Valid |
P -> Q, ~Q |
~P |
Modus tollens |
Valid |
P | Q, ~P |
Q |
Disjunctive syllogism |
Valid |
P -> Q, Q |
P |
Affirming the consequent |
Invalid |
Formula Used
The calculator evaluates an argument with a truth condition. An argument is valid when every assignment that makes all premises true also makes the conclusion true.
Valid ⇔ no row exists where P1 ∧ P2 ∧ ... ∧ Pn is true and C is false.
Implication uses A -> B, which is false only when A is true and B is false. Biconditional uses A <-> B, which is true when both sides have the same truth value. The step engine also applies standard rules, including simplification, double negation, modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, resolution, and biconditional elimination.
How to Use This Calculator
- Enter each premise on its own line.
- Enter the conclusion in the conclusion field.
- Use simple variables, or descriptive labels with underscores.
- Select proof depth and displayed truth table rows.
- Press calculate to view the verdict, derivation, table, and downloads.
For construction work, map each condition to a short symbol. For example, L can mean load is approved. F can mean frame is approved. Then test whether the conclusion follows from the stated inspection rules.
Logic Proofs in Construction Planning
A construction decision often depends on linked conditions. A drawing may need approval before ordering steel. A beam may need inspection before load release. A permit may need clearance before site work starts. These statements form logical premises. A proof checks whether a final claim follows from those premises.
Why Structured Reasoning Helps
Informal notes can hide weak assumptions. A proof table makes each condition visible. It shows every possible truth setting for the symbols. If all premises are true and the conclusion is false in one row, the argument fails. That row is a counterexample. It tells the manager which assumption still needs support.
Using Symbols for Site Rules
Symbols keep the review short. Let P mean concrete passed. Let Q mean formwork can be removed. The rule P -> Q says removal is allowed when the test passes. Adding P lets the proof derive Q by modus ponens. This mirrors a clear approval chain.
Steps and Truth Tables
The calculator uses two checks. The first is a truth table. It scans possible assignments and tests validity. The second is a rule search. It tries common proof moves. These steps explain how a conclusion can be reached. They also show when the proof engine cannot find a short derivation.
Practical Review Habits
Start with one clear meaning for each symbol. Avoid changing that meaning during the proof. Keep premises small. Split large job notes into separate rules. Review any invalid result before rejecting the plan. The counterexample may reveal a missing inspection, a skipped approval, or a condition that was written backwards. Use the output during coordination meetings. Ask whether each premise is verified. Ask who owns each open condition. When a conclusion is valid, record the source documents. When it is invalid, revise the dependency chain carefully today.
Better Records
Download files help with reports. A CSV file stores rows for review. A PDF file gives a compact proof summary. These records can support teaching, quality notes, design checks, and internal audits. The calculator does not replace professional judgment. It supports clearer reasoning before final approval and helps teams discuss logic without guesswork.
FAQs
1. What does this calculator prove?
It checks whether a conclusion follows from given premises. It uses truth tables and a rule-based proof search to explain the result.
2. Which symbols can I use?
You can use ~, &, |, ->, and <->. Words like not, and, or, implies, and iff are also accepted.
3. What is a counterexample?
A counterexample is a truth row where all premises are true, but the conclusion is false. It proves the argument is invalid.
4. Why is my valid proof not derived?
The truth table may show validity, while the rule engine misses a longer derivation. Increase proof depth or rewrite premises in simpler steps.
5. Can I use descriptive variable names?
Yes. Names such as LOAD_OK, PERMIT_READY, and FRAME_PASS work. Avoid spaces inside one symbol.
6. What does vacuous validity mean?
It means the premises cannot all be true together. In classical logic, no counterexample exists, so the argument is valid but inconsistent.
7. Is this suitable for construction decisions?
It helps organize conditional reasoning for approvals, checks, and dependencies. It should support, not replace, expert review and code compliance.
8. What do the downloads include?
The CSV stores premises, verdict, proof steps, and truth rows. The PDF gives a compact summary for records or classroom use.