The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...

concepts. In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. Propositional attitudes are simply attitudes...

of propositional logic, or valid sentences of predicate logic that can be reduced to propositional tautologies by substitution. Propositional logic begins...

This is similar to a way of axiomatizing classical propositional logic. In propositional logic, the inference rule is modus ponens MP: from ϕ → ψ {\displaystyle...

for propositional logic consists of formulas built up from propositional symbols (also called sentential symbols, sentential variables, propositional variables)...

inference. Propositional logic examines the inferential patterns of simple and compound propositions. First-order logic extends propositional logic by articulating...

function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics. Formulas...

classical logic. It consists of propositional logic and first-order logic. Propositional logic only considers logical relations between full propositions. First-order...

propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula...

rule of inference – modus ponens, for propositional logics – or two – with generalisation, to handle predicate logics, as well – and several infinite axiom...

algebraic logic, it became apparent that classical propositional calculus admits other semantics. In Boolean-valued semantics (for classical propositional logic)...

language of propositional calculus, used when talking about propositional calculus) to denote propositions. The semantics of propositional logic rely on truth...

temporal logic include propositional dynamic logic (PDL), (propositional) linear temporal logic (LTL), computation tree logic (CTL), Hennessy–Milner logic, and...

from propositional logic, which does not use quantifiers or relations;: 161  in this sense, propositional logic is the foundation of first-order logic. A...

with Aristotelian term logic, the system of propositional logic developed by the Stoics was one of the two great systems of logic in the classical world...

In mathematical logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula...

propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic statement...

logic Non-monotonic logic Ordered logic Paraconsistent logic Philosophical logic Predicate logic Propositional logic Provability logic Quantum logic Relevance...

specified – see § Propositional inference rules (Suppes–Lemmon style). This section defines the formal syntax for a propositional logic language, contrasting...

are in propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate logic such as first-order logic. In those...

introduction to non-classical propositional logics, which are logical systems that differ from standard classical propositional logic. It covers a wide range...

(e.g., non-classical logic). Although theorems can be written in a completely symbolic form (e.g., as propositions in propositional calculus), they are...

contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set...

classical propositional calculus, each proposition will be assigned a truth value of either true or false. Some systems of classical logic include dedicated...

in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is commonly the case...

between propositional default logic and the following logics have been studied: classical propositional logic; autoepistemic logic; propositional default...

constant Modal operator Propositional calculus Truth-functional propositional logic Roy T. Cook (2009). A Dictionary of Philosophical Logic, p. 294: Truth Function...

a set of propositional formulas and φ a propositional formula, then T ⊢ φ in classical logic if and only if T ⊢ ¬¬φ in intuitionistic logic. In particular...

Mathematics" Chapter II "Symbolic Logic" Part A "The Propositional Calculus" Russell reduces deduction ("propositional calculus") to 2 "indefinables" and...

correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. Logical systems are decidable...