Truth Logic of Modalities Consistent and Incompatible: A Computational Program and Experimental Studies among College Students

Abstract

College students give true judgment routinely, logicians can infer modal inferences, i.e., inferences that concern three alethic modalities; necessary (⸧), possible (◊), and impossible (⟢) from the premises that are logically consistent and incompatible. To achieve the desired results, logicians have intermingled alethic modalities with logical consistency and incompatibility, i.e., necessary consistent, impossible incompatible, possible consistent, or possible incompatible, and write them in classical modal logic as ⸧C (necessary consistent), ◊C (possible consistent) or ◊I (possibly incompatible) and ⟢I (impossible incompatible). M paradigm [Modality, Mental logic theory (MLT), and Mental model theory (MMT)] have been built to enlighten this truth logic. The basic idea of this study is to examine the theory; how do students judge whether two or more different propositions are possible? and, whether their judgment is true. Truth logic is used to construct some principles that help to justify the above theory. First, inferences have either ◊C/ ◊I or ⸧C but assertions are consistent. Second, each ◊C/ ◊I inference and premise is evaluated for both single and double model assertions, and they have consistency (i.e., ⸧C/◊C) and incompatibility (i.e., ◊I or ⟢I). As logicians have predicted, students mostly endorse inferences as ◊C/ ◊I rather than ⸧C and the ⟢I rate is higher in multi-model assertions. Syllogistic logical reasoning with conditionals (if, then...), conjunctions (and), disjunctions (or), and quantifiers “all” and “some” have been used in the M paradigm to evaluate predictions. Moreover, a computational program and experimental studies have strongly supported the all given principles and predictions.