formal systems
[/ˈfɔːrməl ˈsɪstəmz/]
nounpl: formal systems
sistemas formais
1. Structured sets of symbols, rules, and axioms used to generate theorems and proofs in mathematics and logic
Formal systems provide a rigorous foundation for mathematical reasoning and proof theory.
Os sistemas formais fornecem uma base rigorosa para o raciocínio matemático e a teoria da prova.
2. In computer science, abstract models of computation that define how information is processed according to predetermined rules
Formal systems like Turing machines help us understand the limits of computation.
Sistemas formais como máquinas de Turing nos ajudam a entender os limites da computação.
3. Logical frameworks consisting of a language, axioms, and inference rules for deriving conclusions
In formal systems, every statement must be derivable from axioms using specific rules of inference.
Em sistemas formais, toda declaração deve ser derivável dos axiomas usando regras específicas de inferência.
The term 'formal systems' is primarily technical and academic, used in mathematics, logic, and computer science disciplines in both English-speaking countries and Brazil. It carries no regional slang variations and is understood uniformly in educational and professional contexts across these cultures. The concept is fundamental to modern logic and computational theory, originating from early 20th-century developments by mathematicians like David Hilbert.
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