We want to encourage researchers to investigate the potential of proof systems that modify a given set of formulas (e.g., a set of clauses in propositional logic) in a way that preserves satisfiability but not necessarily logical equivalence. We call such modifications interferences, because they can change the models of a given set of formulas. Interferences differ from classical inferences, w...

What is distinctive about my views in epistemology? One thing is that my concern with epistemology is a concern with methodology. Furthermore, I reject psychologism about logic and reject the idea that deductive rules like modus ponens are in any way rules of inference. I accept a kind of methodological conservatism and reject methodological theories that appeal to special foundations, analytic...

This is a tripartite work. The first part is a brief discussion of what it is to be a logical constant, rejecting a view that allows a particular self-referential “constant” • to be such a thing in favour of a view that leads to strong normalisation results. The second part is a commentary on the flattened version of Modus Ponens, and its relationship with rules of type theory. The third part i...

Although the Modus Ponens inference is one of the most basic logical rules, decades of conditional reasoning research show that it is often rejected when people consider stored background knowledge about potential disabling conditions. In the present study we used EEG to identify neural markers of this process. We presented participants with many and few disabler conditionals for which retrieva...

We give a new proof of the following result (originally due to Linial and Post): it is undecidable whether a given calculus, that is a finite set of propositional formulas together with the rules of modus ponens and substitution, axiomatizes the classical logic. Moreover, we prove the same for every superintuitionistic calculus. As a corollary, it is undecidable whether a given calculus is cons...

Since everything is a consequence of an inconsistency, classical logics are not useful in modeling the reasoning of an agent who has inconsistent beliefs. In this paper, we differentiate consistent beliefs from inconsistent beliefs. We propose two belief operators B c and B, standing for consistent belief and belief, respectively. B c has the modus ponens property, by which the agent is able to...

The interpretations of conditionals and conditional inference are often disputed. The classic logic conditional called material implication can easily be proven to be invalid, and the conditional inference rule Modus Ponens represents a tautology that becomes invalid in the face of contrary evidence from realistic scenarios. The foundations of conditionals and conditional inference seem plagued...

The aim of this article is to verify two predictions resulting from the mental models theory of conditional reasoning. First, the denial of antecedent (DA) and modus tollens (MT) inferences should take longer to verify than modus ponens (MP) and af®rmation of consequent (AC) because the former require subjects to ̄esh out the initial model whereas the latter do not. This prediction was con®rmed...

We address an argument by Floridi (2009, 2011), to the effect that digital and analogue are not features of reality, only of modes of presentation of reality. One can therefore have an informational ontology, like Floridi’s Informational Structural Realism, without commitment to a supposedly digital or analogue world. After introducing the topic in Section 1, in Section 2 we explain what the pr...

This paper deals with a new family of (A, N)-implications that derived from fuzzy negation and continuous monotone function, and some properties, like the left neutrally, the exchange principle, the ordering property and the laws of contraposition, of the proposed family of (A, N)-implications are studied. Moreover, the T-conditionality and the Modus tollens for the new family of (A, N)-i...