 The semantic principle of bivalence states that every proposition is either true or false (and not both). Early arguments against bivalence were linked to the problem of determinism. In De Interpretatione (part 9), Aristotle discusses the status of statements about contingent future events, and seems to conclude that for these statements the principle of bivalence should be rejected, otherwise determinism would follow. His argument can be reconstructed as follows. Consider the statement A sea battle will be fought tomorrow. If the statement is true, then the sea battle will necessarily take place. If the sentence is false, then it will be impossible for the sea battle to take place. Assuming that statements are either true or false, one concludes that the sea battle is either necessary or impossible. To escape this fatalistic conclusion Aristotle rejects the principle of bivalence (while possibly retaining the law of excluded middle, see van Fraassen 1966: 493–495, and the entry on  fatalism).  Aristotle’s sea battle argument, although criticized by many, constituted one of Łukasiewicz’ original motivations for the development of his trivalent logic (Łukasiewicz 1920, translated in McCall 1967). Since then various multi-valued logics have been developed where formal disjunction \(\vee\) receives a non-classical interpretation. In Łukasiewicz’ original system, but also in strong Kleene three-valued logic (Kleene 1952), disjunction is interpreted according to the following truth table, where # stands for indefinite or possible in Łukasiewicz, and for undefined in Kleene (Łukasiewicz’s and Kleene’s system differ in their interpretation of implication, we will disregard this issue here).  Priest’s (1979) Logic of Paradox (LP) also adopts the following table for disjunction. There # should be read as both true and false: