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Truth value

Definition

A truth value is the value assigned to a statement according to a logic's semantics. In classical two-valued logic, the possible values are true and false. Other systems can use additional values or degrees, so the applicable rules must always be identified.

What it means

A truth value concerns a proposition rather than an arbitrary string of words. Once the statement and interpretation are clear, its value can be used to evaluate a larger expression. For example, the truth values of two conditions determine the value of their conjunction.

In a classical model, a proposition has a definite truth value even if a particular agent does not know it. The agent's lack of information is not automatically a third classical value. A system can instead represent uncertainty separately or deliberately adopt a different logic.

Software also uses Boolean values for flags and conditions. A flag named Verified may contain true even when a processing error has set it incorrectly. The stored value is part of the program's representation; its name alone does not guarantee a corresponding fact in the world.

How it works

Specify the available values and the rules for the operators. In classical logic, NOT reverses true and false. AND is true only when both inputs are true. Inclusive OR is true when at least one input is true, including when both are true.

For a compound expression, evaluate its parts under the chosen model and combine their values according to the expression's structure. Parentheses matter because they identify which operation applies to which parts. A truth table lists the result for every possible input combination.

Not all systems use the same tables. SQL logical expressions involving NULL can produce an unknown result. For example, true AND unknown is unknown, while false AND unknown is false. Treating NULL as ordinary false can therefore change an application's decisions. Distinguish logical semantics from implementation details such as evaluation order and the representation of missing data.

Three practical examples

• A rules engine combines two recorded eligibility conditions before marking an application ready for review.
• A planning program tests whether a goal formula is true in a represented state.
• A database analyst checks how missing values affect a filter instead of assuming every comparison returns either true or false.

Think of it this way

Think of an indicator panel that displays the result of a condition. A two-state panel has a true position and a false position; another design might also display “unknown”.

The panel's available positions must be defined before interpreting it. The analogy does not make the indicator infallible, and an unknown display is not necessarily halfway between true and false. It can mean that the system lacks the information required by its rules.

Worked example

Evaluating the same expression under different inputs

Let P mean “the request is complete” and Q mean “the reviewer is available”. Evaluate P AND NOT Q in classical logic.

When P=true and Q=true, NOT Q is false, so the result is false.
When P=true and Q=false, NOT Q is true, so the result is true.
When P=false and Q=true, the result is false.
When P=false and Q=false, the result is also false.

Only a complete request with an unavailable reviewer satisfies the expression. This is a condition for a particular queue, not a universal rule about handling requests.

Now suppose Q is NULL in a SQL expression and P is true. NOT Q remains unknown, and true AND unknown is unknown. Replacing Q with false would instead produce true. The substitution changes the meaning by turning missing information into a definite assertion of unavailability.

Illustrative case study

Fictional Maple Scheduling creates a queue for requests that are complete but lack an available reviewer. A data import leaves some reviewer-availability fields missing. The prototype turns every missing value into false, so it places those requests in the queue as if unavailability had been confirmed.

The team gives missing availability an explicit handling path and tests true, false and missing inputs separately. It also distinguishes the administrative action taken when information is missing from the logical claim that a reviewer is unavailable.

This fictional case illustrates how a small assumption about truth values can change workflow behavior. It does not prescribe the correct business action for every missing field.

Common misconceptions and mistakes

• Unknown is always the same as false. That is not true in systems with explicit unknown semantics.
• A probability of 0.7 is a classical truth value. It is an uncertainty measure, not one of classical logic's two values.
• OR always means exactly one condition. Classical inclusive OR also allows both; exclusive OR is a different operation.

Business use

Understanding truth values helps teams review rules, filters and AI-generated conditions before they affect records or decisions. Many defects arise from an unclear meaning for false, a missing-data conversion or a misunderstood operator rather than a sophisticated model failure.

Define each condition, its time scope and its permitted values. Test all relevant input combinations for small rules. When an assistant produces a formula or query, check the semantics of the actual execution environment rather than interpreting the output solely as everyday English.

People also ask

Can there be more than two truth values?

Yes. Some logics introduce additional values or degrees, but their meanings and operator rules must be specified.

Is a truth value the same as a confidence score?

No. Confidence describes uncertainty or model output; its relationship to truth depends on the system.

Does true imply that the system has verified the real world?

No. It may only be the result of evaluating an expression using supplied data.

Check your understanding

In classical logic, P is false and Q is true. What is the truth value of NOT P AND Q?

Answer: True. NOT P is true, and both inputs to AND are therefore true.

Related terms

• Truth
• Conjunction
• Disjunction
• Negation
• Boolean logic
• proposition
• truth table
• three-valued logic
• NULL

Learn next

Read truth tables and Boolean logic. List all four combinations of two Boolean inputs, then compare their AND and OR results with the behavior of unknown values in the database you use.

• Truth

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Sources

Russell and Norvig, Logical Agents, Section 7.4 and its connective truth tables: https://aima.cs.berkeley.edu/4th-ed/pdfs/newchap07.pdf

PostgreSQL project, Logical Operators, including SQL's three-valued tables: https://www.postgresql.org/docs/current/functions-logical.html

The relevant primary textbook and official documentation were read. The request-queue example is an original manual evaluation, not an executed application test.

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