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2. Glossary of logic - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_logic

   The simplest type of formula in logic, consisting of a single predicate applied to a sequence of terms without any logical connectives. atomic sentence A sentence that contains no logical connectives or quantifiers, expressing a basic statement about objects. autological A term that describes itself.

3. Logical grammar - Wikipedia

   en.wikipedia.org/wiki/Logical_grammar

   The foundation of logical grammar was laid out by the Greek philosophers. According to Plato, the task of the sentence is to make a statement about the subject by means of predication. In the Sophist, he uses the example of "Theaetetus is sitting" to illustrate the idea of predication. This statement involves the subject "Theaetetus" and the ...

4. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.

5. Logical reasoning - Wikipedia

   en.wikipedia.org/wiki/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. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water ...

6. Term (logic) - Wikipedia

   en.wikipedia.org/wiki/Term_(logic)

   In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact.

7. Logic - Wikipedia

   en.wikipedia.org/wiki/Logic

   For example, if the formula () stands for the sentence "Socrates is a banker" then the formula articulates the sentence "It is possible that Socrates is a banker". [127] To include these symbols in the logical formalism, modal logic introduces new rules of inference that govern what role they play in inferences.

8. Statement (logic) - Wikipedia

   en.wikipedia.org/wiki/Statement_(logic)

   In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sentences expressing the same ...

9. Logical truth - Wikipedia

   en.wikipedia.org/wiki/Logical_truth

   In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants. Logical constants determine whether a statement is a logical truth when they are combined with a language that limits its meaning.