In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening,...

Substructural type systems are a family of type systems analogous to substructural logics where one or more of the structural rules are absent or only...

extension, the term noncommutative logic is also used by a number of authors to refer to a family of substructural logics in which the exchange rule is inadmissible...

Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening...

meta-theoretic properties of the logic. Logics that deny one or more of the structural rules are classified as substructural logics. Three common structural rules...

Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the...

Bunched logic is a variety of substructural logic proposed by Peter O'Hearn and David Pym. Bunched logic provides primitives for reasoning about resource...

may be viewed as a family of substructural or modal logics. It is generally, but not universally, called relevant logic by British and, especially, Australian...

Relevance logic Sequential logic Spatial logic Strict logic Substructural logic Syllogistic logic Symbolic logic Temporal logic Term logic Topical logic Traditional...

the so-called substructural logics. This system of rules can be shown to be both sound and complete with respect to first-order logic, i.e. a statement...

It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. The...

In computer science, separation logic is an extension of Hoare logic, a way of reasoning about programs. It was developed by John C. Reynolds, Peter O'Hearn...

Stanford University, retrieved 22 March 2024 Restall, Greg (2018), "Substructural Logics", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy...

transformations from any affine space over a field K into itself Affine logic, a substructural logic whose proof theory rejects the structural rule of contraction...

different modal logics, and also for linear and other substructural logics, to give a few examples. However, relatively few systems of modal logic can be formalised...

It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic of commutative bounded integral residuated...

logics of left-continuous t-norms further belong in the class of substructural logics, among which they are marked with the validity of the law of prelinearity...

called the Łukasiewicz–Tarski logic. It belongs to the classes of t-norm fuzzy logics and substructural logics. Łukasiewicz logic was motivated by Aristotle's...

generalization and existential elimination; these occur in substructural logics, such as linear logic. Rule of weakening (or monotonicity of entailment) (aka...

Provability logic Interpretability logic Sequent Sequent calculus Analytic proof Structural proof theory Self-verifying theories Substructural logics Structural...

commutative rings, e.g. the field of real numbers, relevance logics, linear logics, and substructural logics. In the last case, there is no one-to-one correspondence...

In model theory, a branch of mathematical logic, two structures M and N of the same signature σ are called elementarily equivalent if they satisfy the...

Many-valued logic Modal logic Alethic logic Deontic logic Doxastic logic Epistemic logic Temporal logic Paraconsistent logic Substructural logic Metalogic...

species, sometimes with the aid of some kind of many-valued logic or substructural logic. An early attempt in the post-WW2 era to create a mathematical...

the conclusion. Linear logic, which lacks monotonicity and idempotency of entailment. Contraction Exchange rule Substructural logic No-cloning theorem Hedman...

predicate logic of either the classical or intuitionistic flavour, almost any modal logic, and many substructural logics, such as relevance logic or linear...

structures are the objects used to define the semantics of first-order logic, cf. also Tarski's theory of truth or Tarskian semantics. For a given theory...

meaning. substructural logic A class of non-classical logics that relax or modify structural rules found in classical logic, such as relevance logic and linear...

In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose...

used to provide analytic calculi for, e.g., modal, intermediate and substructural logics A hypersequent is a structure Γ 1 ⊢ Δ 1 ∣ ⋯ ∣ Γ n ⊢ Δ n {\displaystyle...