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Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems. Whereas knowledge representation and reasoning ( KRR , KR&R , or KR² ) also aims to understand, reason and interpret knowledge.
Information models can also be expressed in formalized natural languages, such as Gellish. [4] Gellish has natural language variants such as Gellish Formal English and Gellish Formal Dutch (Gellish Formeel Nederlands), etc. Gellish Formal English is an information representation language or semantic modeling language that is defined in the Gellish English Dictionary-Taxonomy, which has the ...
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). [1]
For example, there is no first-order theory whose only model is the real line: any first-order theory with an infinite model also has a model of cardinality larger than the continuum. Since the real line is infinite, any theory satisfied by the real line is also satisfied by some nonstandard models .
When interpreted as a proof within a first-order set theory, such as ZFC, Dedekind's categoricity proof for PA shows that each model of set theory has a unique model of the Peano axioms, up to isomorphism, that embeds as an initial segment of all other models of PA contained within that model of set theory. In the standard model of set theory ...
The model layer is used to monitor a system and to evaluate if the actions are correct, while the control layer determines the actions and brings the system into a goal state. [4] Typical techniques to implement a model are declarative programming languages like Prolog [5] and Golog.
The language was initially developed in support of DARPA Agent Markup Language with a goal of explaining how automated theorem provers (ATP) derive conclusions from a set of axioms. Information, inference steps, inference rules, and agents are the three main building blocks of the language. In the context of an inference step, information can ...
ACL2 – a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition.; Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification.