Frederik Van De Putte

University of Bayreuth and Ghent University · Department(s) of Philosophy (and Moral Science)

jats:title>Abstract We study classical modal logics with pooling modalities , i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relation...

John Rawls famously argued that the Difference Principle would be chosen by any rational agent in the original position. Derek Parfit and Philippe Van Parijs have claimed, contra Rawls, that it is not the Difference Principle which is implied by Rawls’ original position argument, but rather the more refined Lexical Difference Principle. In this pap...

The problem of no hands concerns the existence of so-called responsibility voids: cases where a group makes a certain decision, yet no individual member of the group can be held responsible for this decision. Criteria-based collective decision procedures play a central role in philosophical debates on responsibility voids. In particular, the well-k...

General obligations such as ‘every driver has to give way to a driver coming from the right’ are central in legal reasoning, but have been mostly overlooked in deontic logic. We claim that a simple extension of Standard Deontic Logic to the predicative level is insufficient to capture general obligations. Instead, we argue for an explicit represent...

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 t...

We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of *stit* ('sees to it that') logics of agency. Our full formal language has constants for collective and individual deontic admissibility...

We prove neighbourhood canonicity and strong completeness for the logics $\mathbf {EK}$ and $\mathbf {ECK}$ , obtained by adding axiom (K), resp. adding both (K) and (C), to the minimal modal logic $\textbf {E}$ . In contrast to an earlier proof in [10], ours is constructive. More precisely, we construct minimal characteristic models for both logic...

We introduce classical term-modal logics and argue that they are useful for modelling agent-relative notions of obligation, evidence and abilities, and their interaction with properties of and relations between the agents in question. We spell out the semantics of these logics in terms of neighborhood models, provide sound and strongly complete axi...

Rawls famously claimed that choices based on the Difference Principle coincide with the choices of any rational individual in the Original Position. In this paper, we develop a logic in which we can express and prove Rawls' thesis in its object language. Starting from a standard semantics of choice under uncertainty, we enrich our models in order t...

We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein (Pooling modalities and pointwise intersection: semantics, expressivity, and applications). The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction...

We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in [8]. The definition of our canonical models combines standard techniques with a so-called "puzzle piece construction", which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling...

We prove canonical completeness for the logics EK and ECK, obtained by adding axiom (K), resp. adding both (K) and (C) to the minimal modal logic E. This fills an important gap in the study of classical modal logics and neighbourhood semantics. The proof for EK involves a specific technique to circumscribe the canonical model, and quite some set-th...

We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets N_i (one for each member i of a set G used to interpret the modality □) to a new neighbourhood set NG, which in turn allows us to interpret the operator □_G. Here, X...

Adaptive Logics (ALs) are a viable and useful formal tool to handle various issues in deontic logic. In this paper, we motivate, explain, illustrate, and discuss the use of ALs in deontic logic. Published work on deontic ALs focusses mainly on conflicttolerant deontic logics (logics that can accommodate conflicting obligations) and-to a lesser exte...

Cariani [7] has proposed a semantics for ought that combines two features: (i) it invalidates Inheritance, i.e., the inference from ought(ϕ) to ought(ψ) whenever ψ is logically weaker than ϕ, and it does so in a principled manner; (ii) it allows for coarseness, which means that ought(ϕ) can be true even if there are specific ways of making ϕ true t...

The aim of the present paper is to investigate the logic of holistic detachment , i.e. detachment that is triggered by all and only those circumstances that are fixed (unalterable, unavoidable). To this end, we present the (monotonic) modal logic HD that captures the distinction between mere facts and fixed circumstances, and features a non-normal...

We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets $\mathcal{N}_i$ (one for each member $i$ of a set $G$, used to interpret the modality $\square_i$) to a new neighbourhood set $\mathcal{N}_G$, which in turn allows us...

We present a logic, \(\mathbf {ELI^r}\), for the discovery of deterministic causal regularities starting from empirical data. Our approach is inspired by Mackie’s theory of causes as INUS-conditions, and implements a more recent adjustment to Mackie’s theory according to which the left-hand side of causal regularities is required to be a minimal di...

We show that every indeterministic n-agent choice model \(M^i\) can be transformed into a deterministic n-agent choice model \(M^d\), such that \(M^i\) is a bounded morphic image of \(M^d\). This generalizes an earlier result from Van Benthem and Pacuit [16] about finite two-player choice models. It further strengthens the link between STIT logic a...

We study a logic for deontic necessity and sufficiency (often interpreted as obligation, resp. strong permission), as originally proposed in van Benthem (Bull Sect Log 8(1):36–41, 1979). Building on earlier work in modal logic, we provide a sound and complete axiomatization for it, consider some standard extensions, and study other important proper...

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...

In (Anglberger et al. , 2015, Section 4.1), a deontic logic is proposed which explicates the idea that a formula φ is obligatory if and only if it is (semantically speaking) the weakest permission. We give a sound and strongly complete, Hilbert style axiomatization for this logic. As a corollary, it is compact, contradicting earlier claims from Ang...

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our fr...

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...

Adaptive logics (ALs) in standard format are defined in terms of a monotonic core logic L, a distinct set of ‘abnormal’ formulas Ω and a strategy, which can be either reliability or minimal abnormality. In this article we we ask under which conditions the consequence relation of two ALs that use the same strategy are identical, and when one is a pr...

The standard format of adaptive logics makes use of two so-called strategies: reliability and minimal abnormality. While these are fairly well-known and frequently applied, the question of whether and when the two strategies are equi-expressive has so far remained unaddressed. In this article, we show that for a specific, yet significant class of p...

We investigate a generalization of so-called default-assumption consequence relations, obtained by replacing the consequence relation of classical logic with an arbitrary supraclassical, compact Tarski-logic, and using arbitrary selection functions on sets of sets of defaults. Both generalizations are inspired by various approaches in non-monotonic...

In this paper we argue that an existing theory of concepts called dynamic frame theory, although not developed with that purpose in mind, allows for the precise formulation of a number of problems associated with induction from a single instance. A key role is played by the distinction we introduce between complete and incomplete dynamic frames, fo...

This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation ≺ . They are equivalent to Shoham’s so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms o...

In this article we present the logic MP⊏ that explicates reasoning on the basis of prioritized obligations. Although formal criteria to handle prioritized obligations have been formulated in the literature, little attention has been paid to the actual (non-monotonic) reasoning that makes use of these criteria. The dynamic proof theory of MP⊏ fills...

This article discusses Parikh's axiom of relevance in belief revision, and recalls some results from Kourousias and Makinson (2007, J. Symbolic Logic, 72, 994–1002) in this context. The crucial distinction is emphasized between the uniqueness of the finest splitting of K and the fact that K has several normal forms associated with that finest split...

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])...

This article discusses the proof theory, semantics and meta-theory of a class of adaptive logics, called hierarchic adaptive logics. Their specific characteristics are illustrated throughout the article with the use of one exemplary logic HKx, an explicans for reasoning with prioritized belief bases. A generic proof theory for these systems is defi...

A broad range of defeasible reasoning forms has been explicated by prioritized adaptive logics. However, the relative lack in meta-theory of many of these logics stands in sharp contrast to the frequency of their application. This article presents the first comparative study of a large group of prioritized adaptive logics. Three formats of such log...

This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh's axiom of Relevance. Using one of these logics as an example, we...

In this paper, we present an adaptive logic for deontic conflicts, called P2.1r, that is based on Goble’s logic SDLaPe — a bimodal extension of Goble’s logic P that invalidates aggregation for all prima facie obligations. The logic P2.1r has several advantages with respect to SDLaPe. For consistent sets of obligations it yields the same results as...