Explore insolubilia, the realm of unsolvable problems and paradoxes. Delve into self-reference and logical contradictions, exemplified by the liar paradox,…
An inference rule is a logical structure that permits deriving conclusions from premises. It specifies the valid steps in reasoning,…
An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…
Inconsistent arithmetic refers to a mathematical system where contradictions can be proven, violating the fundamental principle of consistency. This makes…
Inconsistency arises when a system contains contradictory elements, making it impossible for all statements to be true simultaneously. This fundamental…
Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that any consistent system powerful enough for arithmetic will…
The property of a logical or mathematical system where not all true statements can be proven within the system's own…
An implicit definition defines an entity by its relationships to other concepts rather than by direct enumeration of its properties.…
Imperative logic is a formal system for analyzing commands and imperatives, differing from traditional logic focused on declarative statements. It…
Hybrid logic enhances modal logic by allowing direct reference to specific worlds within models. This increases expressiveness, enabling more precise…