|
Logical Relations
Logical relations are a proof method A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof ... employed in programming language semantics to show that two denotational semantics are equivalent. To describe the process, let us denote the two semantics by .html"_;"title="![-">![-!i,_where_i=1,2.__For_each_ ![-!.html"_;"title=".html"_;"title="![-">![-!">.html"_;"title="![-">![-!i,_where_i=1,2.__For_each_data_type">type_A,_there_is_a_particular_associated_binary_relation.html" ;"title="data_type.html" ;"title="">![-!.html" ;"title=".html" ;"title="![-">![-!">.html" ;"title="![-">![-!i, where i=1,2. For each data type">type A, there is a particular associated binary relation">relation \sim between [\![A]\!]_1 and [\![A]\!]_2. This relation is defined such that for each program phrase M, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Method
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
