Search results
Results from the WOW.Com Content Network
A logic that extends first-order logic to allow for more nuanced expressions of quantifier scope and dependence, particularly in contexts of game-theoretical semantics. independent Referring to a pair of propositions that are not contrary , subcontrary , contradictory , logically equivalent , or implied one by the other (either the first by the ...
A predicate in the sense of predicate logic is a sequence of words with clearly defined spaces that becomes a propositional sentence if you insert a proper noun into each space. For example, the word sequence "_ x is a human" is a predicate because it gives rise to the declarative sentence "Peirce is a human" if you enter the proper name ...
First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics.
The word "logic" originates from the Greek word logos, which has a variety of translations, such as reason, discourse, or language. [4] Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences.
A Gödel numbering can be interpreted as an encoding in which a number is assigned to each symbol of a mathematical notation, after which a sequence of natural numbers can then represent a sequence of symbols. These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal ...
In other words, our second rule says "If some sequence of symbols φ (for example, the sequence of 3 symbols φ = '~~p') is a well-formed formula (wff) of L, then the sequence of 2 symbols '~φ' is a well-formed formula (wff) of L". Rule 2 needs to be changed so that the second occurrence of 'φ' (in quotes) be not taken literally.
This well-order, sometimes called shortlex or quasi-lexicographical order, consists in considering first the lengths of the words (if length(a) < length(b), then <), and, if the lengths are equal, using the lexicographical order. If the order on A is a well-order, the same is true for the shortlex order. [2] [3]
Each noun, verb, adjective, adverb, pronoun, preposition and conjunction generates a predicate. Logic forms can be decorated with word senses to disambiguate the semantics of the word. There are two types of predicates: events are marked with e, and entities are marked with x. The shared arguments connect the subjects and objects of verbs and ...