Symmetry and asymmetry between inferences between disjunctions and conditionals

How people make inferences between disjunctions and conditionals is a current important question that can test existing main psychological accounts (mental logic, the probabilistic approach, the original and revised mental model theory) for propositional reasoning. In order to test these accounts, one experiment investigated how relations (material implication, subcontrariety, contradiction, and contrariety) between two basic components (A and C) in disjunctions (e.g., A or C; not-A or C) and conditionals (e.g., if not-A then C; if A then C) and inference directions (disjunction-to-conditional versus conditional-to-disjunction) between disjunctions and their corresponding conditionals affect human inferences between both. It was found that participants’ inferences were symmetric between the two inference directions in compatible relations and incompatible relations where two basic components were on different dimensions, but not in the other relations. Which of the two inference directions was easier depended on relations between two basic components, because some relations tended to elicit particular interpretations of premises and conclusions, or belief biases. The present overall response pattern is beyond all the existing accounts for inferences between disjunctions and conditionals. Inferences between disjunctions and conditionals are complex and so there may not be a unified account for them.

Chasing Hook: Quantified Indicative Conditionals

The chapter looks at indicative conditionals embedded under quantifiers, with a special emphasis on ‘one-case’ conditionals as in No query was answered if it came from a doubtful address. It agrees with earlier assessments that a complete conditional (with antecedent and consequent) is embedded under a quantifier in those constructions, but then proceeds to create a dilemma by showing that we can’t always find the right interpretation for that conditional. Contrary to earlier assessments, Stalnaker’s conditional won’t always do. The chapter concludes that the embedded conditional in the sentence above is a material implication, but the if-clause also plays a pragmatic role in restricting the domain of the embedding quantifier. That an appeal to pragmatics should be necessary at all goes with Edgington’s verdict that ‘we do not have a satisfactory general account of sentences with conditional constituents’.

Super-Strict Implications

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the $$\mathsf{S5}$$-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic.

Spice Behavioral Modeling of TiO2 Memristors for Digital Logic Applications

This work presents a behavior-based memristor model for the simulation of novel digital logic architectures. This model exhibits the nonvolatile hard switching current–voltage curves of the experimentally realized memristors. Because the model is implemented via the widely available traditional SPICE (Simulation Program with Integrated Circuit Emphasis) circuit components, its accuracy is not dependent on still-emerging device transport theory and auxiliary variables. The memristor model is used in material implication (IMPLY) gates to perform both combinational and sequential logics. As IMPLY gates exhibit the complete functionality required for digital logic, this work presents a simple realistic memristor model for use in the simulation of novel digital logic architectures.