Search results
Results from the WOW.Com Content Network
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
Precautionary statements are one of the key elements for the labelling of containers under the GHS, along with: [4] an identification of the product; one or more hazard pictograms (where necessary) a signal word – either Danger or Warning – where necessary; hazard statements, indicating the nature and degree of the risks posed by the product
In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic.
The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...
Material implication does not closely match the usage of conditional sentences in natural language. For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is ...
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
A structure is said to model a set of first-order sentences in the given language if each sentence in is true in with respect to the interpretation of the signature previously specified for . (Again, not to be confused with the formal notion of an " interpretation " of one structure in another) A model of T {\displaystyle T} is a structure that ...
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).