Strong Boethius’ Thesis and Consequential Implication

The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying Aristotle's Thesis (p does not imply not p ) and Weak Boethius' Thesis (if p implies q, then p does not imply not q ). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of Strong Boethius' Thesis (that p implies q implies that p does not imply not q) is identified.     

Two Kinds of Consequential Implication

The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength (symbolized by \(\rightarrow \) and \(\Rightarrow \)). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for \(\Rightarrow \), CI\(\Rightarrow \), is definitionally equivalent to the deontic system KD and is intertranslatable with the minimal consequential system for \(\rightarrow \), CI. The main drawback ot the weaker operator \(\Rightarrow \) is that it lacks unrestricted contraposition, but the final section of the paper argues that \(\Rightarrow \) has some properties which make it a valuable alternative to \(\rightarrow \), turning out especially plausible as a basis for the definition of operators representing synthetic (i.e. context-dependent) conditionals.     

Long-term care reform: An analysis of the proposed federal initiative for long-term care channeling centers

This article investigates alternatives to the current long-term health care system whereby clients would be channeled to appropriate services through community-based long-term care centers. Specifically, it examines whether the federal government should encourage initiatives to develop such a system and reviews three alternative proposals for accomplishing this.     

The Impact of Phantom Decoys on Choices and Perceptions

Phantoms are dominating, attractive alternatives that are unavailable at the time of choice. They occupy different positions in the attribute space, and their unavailability can be either known or unknown to individuals. Although different theories have offered explanations for the influence that phantoms exert on individual choices, they have largely overlooked phantom knowledge. Contradictory predictions can be drawn from these theories, and none provides a good account of the pattern of effects that emerges from our data. We suggest that these contradictions appear because the different theories do not address phantom location and knowledge jointly. When considering phantom knowledge together with location, we observe a consistent overall pattern of effects that encompasses all predictions that could be made on the basis of each theory. We find that known phantoms are stronger when close, and favor the target product, whereas unknown phantoms are stronger when far, and favor the competitor. Finally, we look beyond shifts in choice shares and find that phantom decoys can also affect individuals' post‐choice evaluations and reactions in terms of perceived justice, decision satisfaction, and repatronage intention. Our results show that post‐choice evaluations are driven by phantom knowledge, not phantom location. Copyright © 2012 John Wiley & Sons, Ltd.     

Necessity and Relative Contingency

The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named KΔτ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of Δ and τ allows proving (i) that KΔτ is equivalent to a modal system named K□τ (ii) that both KΔτ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of KΔτ is exactly the deontic system KD. In §4 it is proved that the modal τ -free fragment of a system KΔτw weaker than KΔτ is exactly the minimal normal system K. Presented by Daniele Mundici     

Aristotle's Thesis between paraconsistency and modalization

If the arrow → stands for classical relevant implication, Aristotle's Thesis ¬(A→¬A) is inconsistent with the Law of Simplification (AB)→B accepted by relevantists, but yields an inconsistent non-trivial extension of the system of entailment E. Such paraconsistent extensions of relevant logics have been studied by R. Routley, C. Mortensen and R. Brady. After examining the semantics associated to such systems, it is stressed that there are nonclassical treatments of relevance which do not support Simplification. The paper aims at showing that Aristotle's Thesis may receive a sense if the arrow is defined as strict implication endowed with the proviso that the clauses of the conditional have the same modal status, i.e. the same position in the Aristotelian square. It is so grasped, in different form, the basic idea of relevant logic that the clauses of a true conditional should have something in common. It is proved that thanks to such definition of the arrow Aristotle's Thesis subjoined to the minimal normal system K yields a system equivalent to the deontic system KD.