Formal Logic & Language Constructs¶

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Abstractions that formalize reasoning and symbolic expression — inference rules like existential instantiation, universal generalization, and forward chaining, and logic systems such as modal, three-valued, and equational logic — alongside related linguistic or programming constructs including categorial grammar, predicate abstraction, and typed strings.

20 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

Absolute and relative terms — The terms "bumpy" or "curved", on the other hand, are relative because there is no such thing as "absolute bumpiness" or "absolute curvedness" (although in analytic geometry curvedness is quantified).
Categorial Grammar — Categorial grammar is a family of formalisms in natural language syntax that share the central assumption that syntactic constituents combine as functions and arguments.
Continuous predicate — Continuous predicate is a term coined by Charles Sanders Peirce (1839–1914) to describe a special type of relational predicate that results as the limit of a recursive process of hypostatic abstraction.
Cut Rule — A sequent-calculus inference rule that composes two derivations through a matched intermediate formula, discharging it from the result.
Elvis Operator — In certain computer programming languages, the Elvis operator, often written ?: , is a binary operator that returns the first operand if its value is logically true (according to a language-dependent convention, in other words, a truthy value) or returns its second operand if the first operand is not true.
Equational logic — First-order equational logic consists of quantifier-free terms of ordinary first-order logic, with equality as the only predicate symbol.
Existential Instantiation — In predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form (\exists x) \phi(x) , one may infer \phi© for a new constant symbol c.
Forward chaining — Forward chaining (or forward reasoning) is one of the two main methods of reasoning when using an inference engine and can be described logically as repeated application of modus ponens.
Kripke–Platek set theory with urelements — The Kripke–Platek set theory with urelements (KPU) is an axiom system for set theory with urelements, based on the traditional (urelement-free) Kripke–Platek set theory.
Metric interval temporal logic — In model checking, the Metric Interval Temporal Logic (MITL) is a fragment of Metric Temporal Logic (MTL).
Montague Grammar — Montague grammar is an approach to natural language semantics, named after American logician Richard Montague.
Non-normal modal logic — A non-normal modal logic is a variant of modal logic that deviates from the basic principles of normal modal logics.
Predicate abstraction — In logic, predicate abstraction is the result of creating a predicate from a formula.
S2P (complexity) — In computational complexity theory, S is a complexity class, intermediate between the first and second levels of the polynomial hierarchy.
String (computing) — In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.
Three-valued logic — A three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false, and some third value.
Two-Element Boolean Algebra — In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain.
Uniqueness type — Uniqueness types are implemented in functional programming languages such as Clean, Mercury, SAC and Idris.
Universal generalization — In predicate logic, generalization (also universal generalization, universal introduction, GEN, UG) is a valid inference rule.
Valuation (logic) — In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema.