Quasi-classical logic (QC logic) allows the derivation of non-trivial classical inferences from inconsistent information. A paraconsis-tent, or non-trivializable, logic is, by necessity, a compromise, or weakening , of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in ...

Human conditional reasoning is defeasible: people withdraw logically valid conclusions if they are aware of situations (i.e., exceptions) that prevent the consequent of the rule to happen although the antecedent is given. In this paper we investigate defeasible reasoning with quantified rules. In two experiments we rephrased conditionals from the literature (Experiment 1) and rules from penal c...

Mental model theory (Johnson-Laird & Byrne, 1991) is a dominant theory in human deductive reasoning studies. There are two other classes of theories that deal with human deduction: formal rules theories and content-specific rules theories. This paper begins with a few basic assumptions of the mental model theory, especially those according to which difficulty of inference is proportional to the...

This study presented participants with conditional statements with content that was group-related, container-related, and a combination of group and container. Participants received modus ponens, modus tollens, denying the antecedent, affirming the consequent, and inconsistent forms of conditional arguments. Results demonstrated a significant advantage of the group over the container wording fo...

This study presents evidence for the role of working memory (WM) capacity in the retrieval and inhibition of counterexamples (alternatives and disablers) during everyday conditional reasoning. A total of 292 university students were given a measure of WMcapacity and a reasoning task with everyday, causal conditionals. Results show that the acceptance ratings of the logically valid Modus Ponens ...

Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Ponens and Modus Tollens. Familiar assumptions of familiar truth conditional theories of modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, these explanations go too far. For they foster other predictions of equivoca...

This paper is a critique of version three of Joonmo Kim’s paper entitled “P 6= NP by Modus Tollens.” After summarizing Kim’s proof, we note that the logic that Kim uses is inconsistent, which provides evidence that the proof is invalid. To show this, we will consider two reasonable interpretations of Kim’s definitions, and show that “P 6= NP” does not seem to follow in an obvious way using any ...

Deductive reasoning is traditionally viewed as a unitary process involving either rule-based or visuo-spatial mechanisms. However, there is a disagreement in the neuroimaging literature on whether the data support one alternative over the other. Here we test the hypothesis that discrepancies in the literature result from the reasoning materials themselves. Using functional magnetic resonance im...

According to a higher order reasoning account, inferential reasoning processes underpin the widely observed cue competition effect of blocking in causal learning. The inference required for blocking has been described as modus tollens (if p then q, not q therefore not p). Young children are known to have difficulties with this type of inference, but research with adults suggests that this infer...