rules of inference

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rules of inference

logic

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June 17, 2026

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In logic, an inference is a step from one or more propositions (premises) to a new proposition (conclusion). Rules of inference are truth-preserving, meaning if the premises are true, the conclusion must also be true. This is known as deductive reasoning.12

Two key types of inference are modus ponens and modus tollens.3
* Modus ponens: If A implies B, and A is true, then B is true.
* Modus tollens: If A implies B, and B is false, then A is false.3

Logic also studies ampliative or inductive inferences, which can lead to new information but do not guarantee truth. Fallacies occur when reasoning rules are violated, either in correctness (definitory rules) or efficiency (strategic rules).245

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logic
Definitory and strategic inference rules
There is a further reason why the formulation of systems of rules of inference does not exhaust the science of logic. Rule-governed, goal-directed activities are often best understood by means of concepts borrowed from the study of games. The “game” of logic is…
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There is a further reason why the formulation of systems of rules of inference does not exhaust the science of logic. Rule-governed, goal-directed activities are often best understood by means of concepts borrowed from the study of games. The “game” of logic is…
Read More

formal logic
Natural deduction method in PC
…consists of a set of rules for drawing conclusions from hypotheses (assumptions, premises) represented by wffs of PC and thus for constructing valid inference forms. It also provides a method of deriving from these inference forms valid proposition forms, and in this way it is analogous to the derivation of…
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…consists of a set of rules for drawing conclusions from hypotheses (assumptions, premises) represented by wffs of PC and thus for constructing valid inference forms. It also provides a method of deriving from these inference forms valid proposition forms, and in this way it is analogous to the derivation of…
Read More

history of logic
Syntax and proof theory
…along with a number of rules of inference, characterized equally formally, by means of which one can derive new theorems from existing theorems together with the axioms. The aim of the system is to derive as theorems all of the truths of some part of logic. Such systems are commonly…
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…along with a number of rules of inference, characterized equally formally, by means of which one can derive new theorems from existing theorems together with the axioms. The aim of the system is to derive as theorems all of the truths of some part of logic. Such systems are commonly…
Read More