Modalities, Conditionals, and Values

A Symposium on Philosophical Logic
in Celebration of the Centenary of
Georg Henrik von Wright

Helsinki, Finland, May 23-25, 2016

Abstracts of the talks

Patrick Blackburn: Social Reasoning, Syntactic Recursion and Second-Order False Beliefs


Guglielmo Feis: Jephthah's Predicament and the Limits of Deontic Logic: A Case Study in Direct and Indirect Normative Conflicts

In his Essay in Deontic Logic and the General Theory of Action (1968), von Wright introduced and discussed the predicament of Jephthah (pp. 78-81). The example influenced two different debates in different areas of philosophy: (i) the debate on moral dilemmas in analytic philosophy; (ii) the debate on antinomies in philosophy of law. I merge the two debates by way of analyzing the predicament of Jephthah. I use the von Wrightian predicament to distinguish direct normative conflicts such as antinomy (i.e. conflicts of deontic modalities according to an underlying deontic geometry) from indirect normative conflicts (i.e. cases such as Jephthath or some cases of perplexity by Thomas Aquinas - see Dougherty (2001; 2011)). The paper gives two contributions: (i) I present a topological methodology to map normative conflicts of N-objects that I exemplify for N = 3, i.e antinomies, moral dilemmas and indirect normative conflicts (§2); (ii) I provide a strategy to ground the indirect conflict and explain how some facts can trigger it (§3).

Melvin Fitting: Justifications that Might Be Wrong

In a forthcoming paper, Walter Carnielli and Abilio Rodriguez propose a "Basic Logic of Evidence" whose natural deduction rules are thought of as preserving evidence instead of truth. This turns out to be equivalent to Nelson's paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodriguez understanding of evidence is informal. I provide a formal alternative, using justification logic. First I introduce a modal logic, KX4, in which necessity can be read as asserting there is implicit evidence for, where we understand evidence to permit contradictions. We show N4 embeds into KX4 in the same way that Intuitionistic logic embeds into S4. Then we formulate a new justification logic, JX4, in which the implicit evidence motivating KX4 is made explicit. KX4 embeds into JX4 via a realization theorem. Thus N4 has both implicit and explicit evidence interpretations in a formal sense.

Valentin Goranko: What Deontic Logic Ought To Be, with Insights from von Wright

I will begin with a brief overview of deontic logic, emphasising on von Wright's ideas and contributions to that field and reflecting on some of the fundamental issues and problems that deontic logic has traditionally faced. Eventually, I will argue that deontic logic ought to embrace two essential features:

I will then outline some work in progress towards developing a rich, many-sorted and multi-agent framework for deontic logic.

Andreas Herzig: Logics of intention and means-end reasoning

According to Bratman's influential theory, intentions should be viewed as more or less detailed plans. Such plans are typically made up of high-level actions that cannot be executed directly: they have to be progressively refined to basic actions in order to be executable. Inspired by Shoham's database perspective, we view basic and high-level intentions as organized in an agenda that specifies the temporal intervals within which the corresponding actions have to be performed. Agendas moreover contain beliefs about the environment in terms of beliefs about external events. Actions and events are defined in terms of their pre- and postconditions. High- and lower-level intentions are linked by the instrumentality relation, alias means-end relation. This relation plays a fundamental role in the refinement and the revision of intentions.

Andrea Iacona: Some Doubts about Conjunction Conditionalization

Conjunction conditionalization (CC) is the principle according to which p∧q entails p > q, where p > q is either an indicative conditional or a counterfac- tual. This paper investigates the grounds of CC. More specifically, it focuses on a family of arguments that have been advanced by Walters and Williams in defence of the claim that CC holds for counterfactuals. Its aim is to show that those arguments have a limited reach, both in the case of indicative conditionals and in the case of counterfactuals, as they can work only for a restricted class of interpretations of >.

Dominik Klein and Rasmus K. Rendsvig: A Metric on the Set of Kripke Models

In recent literature, it has been argued that connecting the formal tools of dynamic epistemic logic with the broader mathematical field of dynamical systems theory may be both conceptually important and mathematically fruitful. To see how tight the connection between these fields is, we note that every model transformer in DEL such as a public announcement or a product model naturally gives rise to a discrete-time dynamic system. In this paper, we strengthen connections between DEL and dynamical systems theory by defining a metric on the set of Kripke models which results in a space with desirable properties.

Roman Kuznets: Craig and Lyndon Interpolation Via Labelled Sequent Calculi

The blending of syntactic and semantic methods through correspondence theory has provided both new generic ways of creating analytic cut-free calculi and a novel modular constructive method for proving interpolation properties in modal logics. We show that the two methods can be combined to the mutual benefit by demonstrating that the Craig and Lyndon interpolation properties (IPs) can be proved based on a labelled sequent calculus. We also provide sufficient criteria on the Kripke-frame characterization of a logic that guarantee the IPs. In particular, we show that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs. These criteria capture the modal cube and the infinite family of transitive Geach logics.

Réka Markovich: Order of Norms and Deontic Modality

In Norm and Action (1963) von Wright differentiates first and higher-order norms: norms whose contents are normative acts are higher-order; all others are first-order. The Hungarian Criminal Code imposes a prohibition on homicide. This seems to be a first-order norm: clearly, killing someone is not a normative act. The actual wording of the law, however, reveals only one kind of norm: a requirement for the judge to punish homicide; there is nothing explicit in the wording about a prohibition on homicide. But we understand-and with a plausible semantic theory couched within a general theory of communication, Relevance Theory, we can explain-that it is a prohibition. An outwardly second-order norm is used to create a first-order one-i.e. to assign deontic status to the act it is about, its content-in the natural language of legislation. But this calls von Wright's division between norms of first and higher order into question.

José M. Méndez, Gemma Robles and Francisco Salto: An expansion of Brady's logic BN4 with truth-functional modal operators

The aim of this paper is to investigate a modal expansion of Brady's 4-valued logic BN4. The logic BN4 can be considered as the "4-valued logic of the relevant conditional".

Ilkka Niiniluoto: G. H. von Wright as a Logician


Nicola Olivetti: Neighbourhood Semantics and Labelled Sequent Calculi for Conditional and Doxastic Logics

Neighbourhood semantics can be used to give a simple and transparent semantics to logical systems characterised by Standard Kripke relational semantics. We analyse two related cases : Preferential Conditional logic and Conditional Doxastic logic by Board, Baltag and Smets. Basing on the neighbourhood semantics, we develop labelled sequent calculi for the respective logics. The calculi are well-behaved proof-theoretically and they provides a decision procedure, whence a constructive proof of the finite model property. [Joint work with Sara Negri, Marianna Girlando and Vincent Risch]

Eugenio Orlandelli and Sara Negri: Proof Theory for Quantified Non-normal Modal Logics

This paper provides the first proof-theoretic study of quantified non-normal modal logics. It introduces labelled sequent calculi for the first order extension, both with free and with classical quantification, of all the logics in the cube of non-normal modal logics, as well as of some interesting extensions thereof, and it studies the role of the Barcan Formulas in these calculi. It will be shown that the calculi introduced have good structural properties: they have invertibility of the rules, height-preserving admissibility of weakening and contraction, and syntactic cut elimination. It will also be shown that each of the calculi introduced is sound and complete with respect to the appropriate class of neighbourhood frames with either constant or varying domains. In particular the completeness proof constructs a formal proof for derivable sequents and a countermodel for underivable ones, and it gives a semantic proof of the admissibility of cut.

Eric Pacuit: A modal logic of beliefs with interpretation shifts

The Brandenburger-Keisler paradox shows that there are certain configurations of interactive beliefs among two agents that cannot be represented in any Kripke model. This has important ramifications for the epistemic foundations of game theory. In this talk, I will develop a new modal logic to formalize the Brandenburger-Keisler paradox in which the interpretation of a formula may vary from world to world. The formalization of the BK paradox in this logical framework reveals interesting connections between the BK paradox and Montague and Kaplan's Knower Paradox.

Gabriella Pigozzi: Changing Norms: A Framework for Revising and Contracting Rules


Gemma Robles: The 4-valued logic of entailment E4

In the present paper, we introduce the 4-valued logic of entailment E4. The logic E4 is related to Brady's BN4 in a similar way to which Anderson and Belnap's logic of entailment E is related to their logic of the relevant conditional R: while BN4 can be considered as the "4-valued logic of the relevant conditional", E4 can be viewed as the "4-valued logic of relevant entailment".

Gabriel Sandu: Ceteris Paribus Modalities


Giovanni Sartor: Normative acts, norms and normative propositions in a ceteris paribus deontic logic

This paper builds upon two major strands of Georg H. von Wright's research: deontic logic and the logic of preferences. On this basis a solution is proposed for some issues emerging from his work. Firstly, how to reconcile norm-positivism (each norm is based on a social fact) and valid deontic inference (obligations and permission may hold on the basis of valid deductions). Secondly, how to overcome the apparently counterintuitive consequences of deontic logic, the so called deontic paradoxes. We shall address the first issue by arguing that valid normative acts generate institutional ceteris-paribus preferences over possible words, and that on the basis of these preferences it is possible to assign truth values to normative proposition, and develop deontic inferences. We shall address the second issue by showing that a deontic logic whose semantics is based on ceteris paribus preferences can avoid the paradoxes of standard deontic logic.

Cesar Antonio Serbena: G. H. von Wright on Non-classical Logics

The article exposes and discusses the philosophical view that von Wright had on non-classical logics and had to obtain the truth-logics. His justifications for his choice of certain axioms are also exposed. The main point analysed is the relation between the paracomplete and paraconsistent truth-logic of von Wright and the general paraconsistent logics. The conclusion is that non-classical logics presuppose a general theory of logic negation.

Annika Siders: Notes on Gödel's ontological proof

We state some causes for the modal collapse of Gödel's ontological proof by examining its proof and give a proof of monotheism from the axioms.

Gustavo Vieira Vilar Garcia: From Action to Proposition in von Wright's Deontic Systems

Georg Henrik von Wright signaled in his first major attempt of formalizing normative concepts (Deontic Logic, 1951) that norms had to do with actions in the first place, and only reflexively concerned demanded states of affairs. Symbolically, this meant deontic operators were applied primarily to letters representing generic actions. In the following steps taken by the discipline, however, this standpoint was substantially forsaken in favor of a more traditional approach that regarded norms as commands for the actualization of states of affairs. Von Wright, himself, endorsed this deviation from his original project. This work intends to investigate why deontic logic took the propositional and modal course of development over the agential proposal, offering explanatory reasons.

Berislav Žarnić: Von Wright's Pragmatics Turn in Deontic Logic

In his later works on deontic logic von Wright put forward a programmatic statement on its nature: it is "a study of conditions which must be satisfied in rational norm-giving activity". In this new perspective the axioms of standard deontic logic are to be read as descriptions of "perfection properties" that a normative system should have and to which there correspond second-order obligations, or requirements of rationality to which the norm-giver is subordinated in the norm-giving activity. A simple formal explication for von Wright's programmatic statement can be obtained using the set-theoretic approach proposed by many philosophical logicians according to which the existence of an obligation-norm within a normative system is represented by the membership of its propositional content in the set that represents the normative system in question. The translation from the language of standard deontic logic (without iterated operators) to the set-theoretic language confirms the claims put forward by von Wright in 1999, but the translation also suggests the extension of the meta-normative approach to other norm-related activities. Consequently, the distinction must be introduced between perfection properties of obligation-norm sets with respect to the activity of the norm-giver and the reasoning of the norm-recipient. For example, the norm-giver is under obligation to enunciate consistent normative systems but not deductively closed ones. On the other hand, the norm-recipient has the obligation to reason on the basis of the normative system and thus to treat it as a deductively closed set, while having no obligation with respect to its consistency. In this way von Wright's last remarks on deontic logic open up a new perspective which asks for the logical pragmatics. In addition to this and taking into account von Wright's thesis on only normative and not conceptual relation between permission and absence of prohibition, the translation of deontic postulates can also be extended to the description of the properties of the "counter-set", the set of that which is either forbidden or optional. The extended translation reveals that perfection properties come in pairs and provides an interesting way for understanding the relation of the norm-recipient to an inconsistent norm-set or to a normative system whose norm-set and counter-set are not disjunctive. The power of revision does not belong to the norm-recipient role. A normative vacuum does not appear if the norm-recipient is subordinated to an inconsistent normative system in which there is no way out of the normative conflict on the basis of the metanormative principles on the priority order over norms. In such a case it seems plausible to postulate the second-order norm for the reasoning of the norm-recipient according to which a shift to an inconsistency-tolerant logic is required.