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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.
In first-order logic, converting predicates to functions is called reification; for this reason, fluents represented by functions are said to be reified. When using reified fluents, a separate predicate is necessary to tell when a fluent is actually true or not.
The fluent calculus is a formalism for expressing dynamical domains in first-order logic. It is a variant of the situation calculus; the main difference is that situations are considered representations of states. A binary function symbol is used to concatenate the terms that represent facts that hold in a situation.
SPASS is a first-order logic theorem prover with equality. This is developed by the research group Automation of Logic, Max Planck Institute for Computer Science . The Theorem Prover Museum [ 27 ] is an initiative to conserve the sources of theorem prover systems for future analysis, since they are important cultural/scientific artefacts.
The store could act as a knowledge base and the clauses could act as rules or a restricted form of logic. As a subset of first-order logic Prolog was based on Horn clauses with a closed-world assumption—any facts not known were considered false—and a unique name assumption for primitive terms—e.g., the identifier barack_obama was ...
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving and computational linguistics. [1] [2] [3]Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and rules, which define relations.
There are three common ways of handling this in first-order logic: Use first-order logic with two types. Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for ...
AIMA gives detailed information about the working of algorithms in AI. The book's chapters span from classical AI topics like searching algorithms and first-order logic, propositional logic and probabilistic reasoning to advanced topics such as multi-agent systems, constraint satisfaction problems, optimization problems, artificial neural networks, deep learning, reinforcement learning, and ...