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X-bar theory graph of the sentence "He studies linguistics at the university." Constituency is a one-to-one-or-more relation; every word in the sentence corresponds to one or more nodes in the tree diagram. Dependency, in contrast, is a one-to-one relation; every word in the sentence corresponds to exactly one node in the tree diagram.
Hence the alpha graphs are a minimalist notation for sentential logic, grounded in the expressive adequacy of And and Not. The alpha graphs constitute a radical simplification of the two-element Boolean algebra and the truth functors. The depth of an object is the number of cuts that enclose it. Rules of inference:
The premises are shown above a line, called the inference line, [15] separated by a comma, which indicates combination of premises. [44] The conclusion is written below the inference line. [ 15 ] The inference line represents syntactic consequence , [ 15 ] sometimes called deductive consequence , [ 45 ] which is also symbolized with ⊢.
a sentence justified by the citation of (1) a rule of inference and (2) the prior line or lines of the proof that license that rule. Introducing a new assumption increases the level of indentation, and begins a new vertical "scope" bar that continues to indent subsequent lines until the assumption is discharged.
A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic.. In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate in a prescribed way. In particular, if the vertex set of the graph is V , one should be able to choose a word w over the alphabet V such that letters a and b alternate in w if and only if the ...
In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G).
Consider the formal sentence . For some natural number , =.. This is a single statement using existential quantification. It is roughly analogous to the informal sentence "Either =, or =, or =, or... and so on," but more precise, because it doesn't need us to infer the meaning of the phrase "and so on."