1. A machine implemented method of executing four-valued logic in a semantic network, the method comprising: defining a logic system having a NOT logical connective denoted as “ ” an AND logical connective denoted as “ ,” and an OR logical connective denoted as “v,” wherein false values are represented with an “F” symbol, true values are represented by a “T” symbol, undefined values are represented by a “U” symbol, and defined values are represented by a “D” symbol, such that for a property P false values are in a set { P}, true values are in a set {P}, undefined values are in a set { }, defined values are in a set {P, P}, wherein said logic system is proven complete and w-consistent by a set of statements comprising: F is T, T is F, U is D, D is U; F F is F, F T is F, F U is F, F D is F; T F is F, T T is T, T U is U, T D is D; U F is F, U T is U, U U is U, U D is F; D F is F, D T is D, D U is F, D D is D; FvF is F, FvT is T, FvU is U, FvD is D; TvF is T, TvT is T, TvU is T, TvD is T; UvF is U, UvT is T, UvU is U, UvD is T; and DvF is D, DvT is T, DvU is T, DvD is D; generating a semantic network representing digitally stored information, said semantic network comprising a plurality of object nodes and a plurality of relationships between said plurality of object nodes, by: providing a first vector and a second vector in digital memory for each of said plurality of object nodes, each of said first vector and said second vector being a dynamically allocated array having a plurality of index positions each with a size of one bit; linearly encoding semantic information for an object node by storing two bits that together encode a false value, true value, undefined value, or defined value, a first bit of said two bits being stored at an index position within the first vector associated with the object node, and a second bit of said two bits being stored at the same index position within the second vector associated with the object node; linearly encoding syntactic information associated with said plurality of relationships in said digital memory; and testing conditionals or quantifying variables in said semantic network during successive recursive steps in a predicate calculus using said logic system, the false values, true values, undefined values, and defined values in the semantic information associated with said plurality of object nodes, and the syntactic information associated with said plurality of relationships, and a phrase structure rewrite rule on said plurality of object node; and using a top/down, bottom/up parser to syntactically parse grammar within said semantic network, by marking subsets of said plurality of object nodes as {S} for start, {Np} for a noun phrase, {Vp} for verb a phrase and {Pp} for a prepositional phrase (predicate participant), and marking each of said plurality of object nodes as {N} for a noun, {V} for a verb, {det} for a determinant and {prep} for a preposition, wherein linear encoding of said semantic information and said syntactic information optimizes short term memory, maximizes long term storage, and optimizes communication and memory between different knowledge sources or processes.