Arthur Norman Prior was born on 4 December 1914 in Masterton, New Zealand. He studied philosophy in the 1930s and was a significant, and often provocative, voice in theological debates until well into the 1950s. He became a lecturer in philosophy at Canterbury University College in Christchurch in 1946 succeeding Karl Popper. He became a full professor in 1952. He left New Zealand permanently for England in 1959, first taking a chair in philosophy at Manchester University, and then becoming a fellow of Balliol College, Oxford, in 1966. Prior died on 6 October 1969 in Trondheim, Norway. After Prior’s death, many logicians and philosophers have analysed and discussed his approach to formal and philosophical logic. In particular, his contributions to modal logic, tense-logic and deontic logic have been studied.
In 1957, A.N. Prior proposed the three-valued modal logic Q as a ‘correct’ modal logic from his philosophical motivations, see Prior (1957). Prior developed Q in order to offer a logic for contingent beings, in which one could intelligibly and rationally state that some beings are contingent and some are necessary, see Akama & Nagata (2005). According to Akama & Nagata (2005), Q has a natural semantics. In other words, from the philosophical point of view, Q can be regarded as an ‘actualist’ modal logic.
This review article is a developed description of, and discussion on, ‘The System Q’ that is the fifth chapter of Prior (1957). In addition, in his logical analysis of ‘Time & Existence’ (that is the eights chapter of Prior (1967)), Prior has worked on system Q. Thus, Prior (1967) has also been very useful for this article. This article analyses the logical structure of system Q in order to provide a more understandable description as well as logical analysis for today’s logicians, philosophers, and information-computer scientists. In the paper, the Polish notations are translated into modern notations in order to be more comprehensible and to support the developed formal descriptions as well as semantic analysis.