Grafting Hypersequents onto Nested Sequents

We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics $\mathsf{K5}$ and $\mathsf{KD5}$, as well as for extensions of the modal logics $\mathsf{K}$ and $\mathsf{KD}$ with the axiom for shift reflexivity. The latter of these extensions is also known as $\mathsf{SDL}^+$ in the context of deontic logic. All our calculi enjoy syntactic cut elimination and can be used in backwards proof search procedures of optimal complexity. The tableaufication of the calculi for $\mathsf{K5}$ and $\mathsf{KD5}$ yields simplified prefixed tableau calculi for these logic reminiscent of the simplified tableau system for $\mathsf{S5}$, which might be of independent interest

The Role of Deontic Logic in the Specification of Information Systems

In this paper we discuss the role that deontic logic plays in the specification of information systems, either because constraints on the systems directly concern norms or, and even more importantly, system constraints are considered ideal but violable (so-called `soft¿ constraints).\ud To overcome the traditional problems with deontic logic (the so-called paradoxes), we first state the importance of distinguishing between ought-to-be and ought-to-do constraints and next focus on the most severe paradox, the so-called Chisholm paradox, involving contrary-to-duty norms. We present a multi-modal extension of standard deontic logic (SDL) to represent the ought-to-be version of the Chisholm set properly. For the ought-to-do variant we employ a reduction to dynamic logic, and show how the Chisholm set can be treated adequately in this setting. Finally we discuss a way of integrating both ought-to-be and ought-to-do reasoning, enabling one to draw conclusions from ought-to-be constraints to ought-to-do ones, and show by an example the use(fulness) of this

Computer Science and Metaphysics: A Cross-Fertilization

Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational philosophy with a focus on metaphysics. In this paper, we (a) develop results in modal metaphysics whose discovery was computer assisted, and (b) conclude that these results work not only to the obvious benefit of philosophy but also, less obviously, to the benefit of computer science, since the new computational techniques that led to these results may be more broadly applicable within computer science. The paper includes a description of our background methodology and how it evolved, and a discussion of our new results.Comment: 39 pages, 3 figure

Metaphysical and absolute possibility

It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense.” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it

Enriching Deontic Logic

It is well known that systems of action deontic logic emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law are subject to paradoxes. In general, paradoxes are acknowledged as such if we have intuitions telling us that things should be different. The aim of this paper is to introduce a paradox-free deontic action system by (i) identifying the basic intuitions leading to the emergence of the paradoxes and (ii) exploiting these intuitions in order to develop a consistent deontic framework, where it can be shown why some phenomena seem to be paradoxical and why they are not so if interpreted in a correct way

FIVE STEPS TO RESPONSIBILITY

Responsibility has entered the academic discourse of logicians hardly more than few decades ago. I suggest a logical concept of responsibility which employs ideas both from a number of theories belonging to different branches of logic as well from other academic areas. As a comment to this concept, I suggest five steps narrative scenario in order to show how the logical dimension of responsibility emerges from diverse tendencies in logic and other sciences. Here are the five steps briefly stated: Step 1. Developing modal formalisms capable of evaluative analysis of situations (deontic, epistemic and etc.). Step 2. Drawing a conceptual borderline between normal and non-normal (weak) logical systems. Step 3. Using different kinds of models. Step 4. Agent- and action- friendly turn in logic. Step 5. Creating formalisms for modeling different types of agency. An idea advocated here within 5-Steps route to responsibility is that this concept is a complex causal and evaluative (axiological) relation. A logical account may be given for causal and normative aspects of this relation. Unfolding the responsibility back and forth through 5 Steps will result in different concepts. The technicalities are minimized for the sake of keeping the philosophical scope of the paper. For the same reason I also refrain from discussing legal and juridical ramifications of the issue

A structured argumentation framework for detaching conditional obligations

We present a general formal argumentation system for dealing with the detachment of conditional obligations. Given a set of facts, constraints, and conditional obligations, we answer the question whether an unconditional obligation is detachable by considering reasons for and against its detachment. For the evaluation of arguments in favor of detaching obligations we use a Dung-style argumentation-theoretical semantics. We illustrate the modularity of the general framework by considering some extensions, and we compare the framework to some related approaches from the literature.Comment: This is our submission to DEON 2016, including the technical appendi