Deontic logicDeontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses OA to mean it is obligatory that A (or it ought to be (the case) that A), and PA to mean it is permitted (or permissible) that A, which is defined as .
Epistemic modal logicEpistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C.
Modal operatorA modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not.
Method of analytic tableauxIn proof theory, the semantic tableau (tæˈbloʊ,_ˈtæbloʊ; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. Computation constructs this tree and uses it to prove or refute the whole formula. The tableau method can also determine the satisfiability of finite sets of formulas of various logics.
Accessibility relationAn accessibility relation is a relation which plays a key role in assigning truth values to sentences in the relational semantics for modal logic. In relational semantics, a modal formula's truth value at a possible world can depend on what's true at another possible world , but only if the accessibility relation relates to . For instance, if holds at some world such that , the formula will be true at . The fact is crucial. If did not relate to , then would be false at unless also held at some other world such that .
Strict conditionalIn logic, a strict conditional (symbol: , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For any two propositions p and q, the formula p → q says that p materially implies q while says that p strictly implies q. Strict conditionals are the result of Clarence Irving Lewis's attempt to find a conditional for logic that can adequately express indicative conditionals in natural language.
Paradoxes of material implicationThe paradoxes of material implication are a group of true formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated as "if ... then ...". A material conditional formula is true unless is true and is false. If natural language conditionals were understood in the same way, that would mean that the sentence "If the Nazis had won World War Two, everybody would be happy" is vacuously true.
Norm (philosophy)Norms are concepts (sentences) of practical import, oriented to affecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply "ought-to" types of statements and assertions, in distinction to sentences that provide "is" types of statements and assertions. Common normative sentences include commands, permissions, and prohibitions; common normative abstract concepts include sincerity, justification, and honesty.
Classical modal logicIn modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators that is also closed under the rule Alternatively, one can give a dual definition of L by which L is classical if and only if it contains (as axiom or theorem) and is closed under the rule The weakest classical system is sometimes referred to as E and is non-normal. Both algebraic and neighborhood semantics characterize familiar classical modal systems that are weaker than the weakest normal modal logic K.
Dynamic logic (modal logic)In logic, philosophy, and theoretical computer science, dynamic logic is an extension of modal logic capable of encoding properties of computer programs. A simple example of a statement in dynamic logic is which states that if the ground is currently dry and it rains, then afterwards the ground will be wet. The syntax of dynamic logic contains a language of propositions (like "the ground is dry") and a language of actions (like "it rains").
