Frederik Van De Putte

This paper introduces a new format for reasoning with prioritized standards of normality. It is applicable in a broad variety of contexts, e.g. dealing with (possibly conflicting) prioritized belief bases or combining different reasoning methods in a prioritized way. The format is a generalization of the standard format of adaptive logics (see [4]). Every logic that is formulated within it has a straightforward semantics in the style of Shoham's selection semantics (see [22]) and a dynamic proof theory. Furthermore, it can count on a rich meta-theory that inherits the attractive features of the standard format, such as soundness and completeness, reflexivity, idempo-tence, cautious monotonicity, and many other properties. © 2013 Elsevier B.V., All rights reserved.

The standard format for adaptive logics offers a generic and unifying formal framework for defeasible reasoning forms. One of its main distinguishing features is a dynamic proof theory by means of which it is able to explicate actual reasoning. In many applications it has proven very useful to superpose sequences of adaptive logics, such that each logic treats the consequence set of its predecessor as premise set. Although attempts have been made to define dynamic proof theories for some of the resulting logics, no generic proof theory is available yet. Moreover, the existing proof theories for concrete superpositions are sub-optimal in various respects: the derivability relations characterized by these proposals are often not adequate with respect to the consequence relation of the superposed adaptive logics and in some cases they even trivialize premise sets. An adequate and generic proof theory is needed in order to meet the requirement of explicating defeasible reasoning in terms of superpositions of adaptive logics. This paper presents two equivalent generic proof theories for superpositions of adaptive logics in standard format. By means of simple examples, the basic ideas behind these proof theories are illustrated and it is shown how the older proposals are inadequate. © 2016 Elsevier B.V., All rights reserved.

When our current beliefs face a certain problem - e.g. when we receive new information contradicting them-, then we should not remove beliefs that are not related to this problem. This principle is known as "minimal mutilation" or "conservativity" [21]. To make it formally precise, Rohit Parikh [32] defined a Relevance axiom for (classical) theory revision, which is based on the notion of a language splitting. I show that both concepts can and should be applied in a much broader context than mere revision of theories in the traditional sense. First, I generalize their application to belief change in general, and strengthen the axiom of relevance in order to make it fully syntax-independent. This is done by making use of the least letter-set representation of a set of formulas [27]. Second, I show that the logic underlying both concepts need not be classical logic and establish weak sufficient conditions for both the finest splitting theorem from [25] and the least letter-set theorem from [27]. Both generalizations are illustrated by means of the paraconsistent logic CLuNs and compared to ideas from [14, 36, 24]. © 2016 Elsevier B.V., All rights reserved.

This paper makes a twofold contribution to the study of expressivity in modal logic. First, we introduce and study the novel concept of conditional expressivity. Second, we use the concept to explore inferential relations between collective deontic admissibility statements for different groups. Negative results on conditional expressivity are stronger than standard (unconditional) inexpressivity results: we show that the well-known inexpressivity results from epistemic logic on distributed knowledge and on common knowledge only concern unconditional expressivity. By contrast, we prove negative results on conditional expressivity in the deontic logic of collective agency. In particular, we consider the full formal language of the deontic logic of collective agency, define a natural class of sublanguages of the full language, and prove that a collective deontic admissibility statement about a particular group is conditionally expressible in a sublanguage from the class if and only if that sublanguage includes a collective deontic admissibility statement about a supergroup of that group. Our negative results on conditional expressivity may serve as a proof of concept for future studies of expressivity in modal logic.

Abduction of generalizations is the process in which explanatory hypotheses are formed for generalizations such as “pineapples taste sweet” or “rainbows appear when the sun breaks through the rain”. This phenomenon has received little attention in formal logic and philosophy of science. The current paper remedies this lacuna by first giving an overview of some general characteristics of this process, elaborating on its ubiquity in scientific and everyday reasoning. Second, the adaptive logic LA∀ is presented to explicate this process formally.La abducción de generalizaciones es el proceso en el que se forman hipótesis explicativas para generalizaciones tales como "las piñas saben dulce" o "el arcoiris aparece cuando el sol sale a través de la lluvia". Este fenómeno ha recibido poca atención tanto en lógica formal como en filosofía de la ciencia. Este artículo viene a llenar este hueco. En primer lugar, ofrecemos una panorámica de algunas características generales de este proceso, analizando su ubicuidad en el razonamiento científico y cotidiano. En segundo lugar, se presenta la lógica adaptativa LA∀ para dar una explicación formal de este proceso.

We study original position arguments in the context of social choice under ignorance. First, we present a general formal framework for such arguments. Next, we provide an axiomatic characterization of social choice rules that can be supported by original position arguments. We illustrate this characterization in terms of various well-known social choice rules, some of which do and some of which do not satisfy the axioms in question. Depending on the perspective one takes, our results can be used to argue against certain rules, against Rawlsian theories of procedural fairness, or in support of richer, multidimensional models of individual choice.

Methodological individualists often claim that any social phenomenon can ultimately be explained in terms of the actions and interactions of individuals. Any Nagelian version of methodological individualism requires that there be bridge laws that translate social statements into individualistic ones. We show that Nagelian individualism can be put to logical scrutiny by making the relevant social and individualistic languages fully explicit and mathematically precise. In particular, we prove that the social statement that a group of (at least two) agents performs a deontically admissible group action cannot be expressed in a well-established deontic logic of agency that models every combination of actions, omissions, abilities, and obligations of finitely many individual agents.

This book explores some of Kit Fine's outstanding contributions to logic, philosophy of language, philosophy of mathematics, and metaphysics, among others. Contributing authors address in-depth issues about truthmaker semantics, counterfactual conditionals, grounding, vagueness, non-classical consequence relations, and arbitrary objects, offering critical reflections and novel research contributions. Each chapter is accompanied by an extensive commentary, in which Kit Fine offers detailed responses to the ideas and themes raised by the contributors. The book includes a brief autobiography and exhaustive list of his publications to this date. This book is of interest to logicians of all stripes and to analytic philosophers more generally.