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A variety of basic concepts is used in the study and analysis of logical reasoning. Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case.
A paradox in deontic logic arising from imperatives that imply counterintuitive obligations, demonstrating challenges in formalizing moral and ethical reasoning. rule of inference A logical rule that justifies the transition from a set of premises to a conclusion, forming the basis of deductive reasoning. rule of replacement
Computational logic is the branch of logic and computer science that studies how to implement mathematical reasoning and logical formalisms using computers. This includes, for example, automatic theorem provers , which employ rules of inference to construct a proof step by step from a set of premises to the intended conclusion without human ...
An argument, more fully a premise–conclusion argument, is a two-part system composed of premises and conclusion. An argument is valid if and only if its conclusion is a consequence of its premises. Every premise set has infinitely many consequences each giving rise to a valid argument.
Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning. With historical origins in logic , dialectic , and rhetoric , argumentation theory includes the arts and sciences of civil debate, dialogue , conversation , and persuasion .
Deductive inference is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added. By contrast, everyday reasoning is mostly non-monotonic because it involves risk: we jump to conclusions from deductively insufficient premises.
In logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
For the most part this discussion of logic deals only with deductive logic. Abductive reasoning is a form of inference which goes from an observation to a theory which accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not ...