On the third forms of conjunction and disjunction in logic with vector semantics

The paper introduces the concepts of informational and native contradictions. Informational contradiction is understood as the inconsistency of a resulting from discrepancies in information sources, while native contradiction describes a situation where a statement is simultaneously true and false in the same respect (i.e., the contradiction is inherent to the object). Based on the concept of native contradiction within the class of logic with vector semantics, the third forms of conjunction and disjunction (native conjunction and disjunction) are defined for the first time as an extension to the known first and second forms, along with other native connectives and relations. Several properties of these forms are examined, including the applicability of de Morgan's laws when combined with the first form of negation, commutativity, and the distinct role of the truth vector "uncertainty." It is also noted that while these forms are defined under the assumption of a native contradiction, they, along with other native connectives and relations, may be useful for decision-making in contexts of informational contradictions. Qubits, which serve as the foundation of quantum information processing, are cited as an example of a native contradiction.