In non-classical logic systems, the truth tables for logical connectives may differ from those in classical logic, allowing for a wider range of logical possibilities.

Implication is a common type of connective in propositional non-classical logic, and its truth table can vary depending on the specific non-classical logic system.

Modal Logic is a non-classical logic system that introduces operators for possibility and necessity, allowing for reasoning about what is possible or necessary in a given situation.

In fuzzy logic, truth values are typically assigned to propositions within the range [0, 1], where 0 represents absolute falsity and 1 represents absolute truth, with intermediate values representing varying degrees of truth.

Intuitionistic Logic is a non-classical logic system that rejects the law of excluded middle, which states that a proposition must be either true or false. This allows for the possibility of propositions that are neither true nor false.

Paraconsistent logic allows for the coexistence of contradictory propositions within a single logical system, without necessarily leading to the collapse of the entire system.

Quantum Logic is a non-classical logic system that is closely related to quantum mechanics and is used to reason about quantum phenomena, such as superposition and entanglement.

Relevance logic focuses on the relevance of the propositions connected by logical connectives, rather than solely on their truth values.

Fuzzy Logic allows for truth values that can be partially true and partially false, representing intermediate degrees of truth.

Free logic allows the user to define the truth tables of logical connectives freely, providing a high degree of flexibility in logical reasoning.

Doxastic Logic is a non-classical logic system that focuses on reasoning about beliefs and knowledge, allowing for the representation and manipulation of beliefs and their relationships.

Linear logic imposes a restriction on the use of logical connectives, requiring that they be used in a balanced way, meaning that each connective must be matched with its corresponding dual connective.

Deontic Logic is a non-classical logic system that focuses on reasoning about actions and their consequences, allowing for the representation and manipulation of obligations, permissions, and other normative concepts.

Many-valued logic allows for an infinite number of truth values, expanding the range of possible logical values beyond the traditional true and false.

Fuzzy Logic is a non-classical logic system that is designed to handle vagueness and uncertainty by allowing for truth values that can be partially true and partially false.