This paper traces the intellectual effects of an encounter between Stig Kanger and Donald Davidson -two very different philosophers working in two seemingly unconnected areas. Their meeting in Oslo 1979 led the latter to improve his influential theory of radical interpretation and gave the former an inspiration for a rather striking paradox in preference logic. But, as we show, the paradox can be dis-solved and the radical interpretation continues to confront serious difficulties. Simultaneous elicitation of a speaker’s meaning, (...) beliefs and desires merely from his attitudes to sentences in the language he uses is a very ambitious project, but its theoretic viability is strongly questionable. (shrink)

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more abstract sense, preference orderings are used in conditional logic or non-monotonic reasoning as a way of arranging worlds into more or less plausible ones. The field of preference (...) logic (cf. Hansson [10]) studies formal systems that can express and analyze notions of preference between various sorts of entities: worlds, actions, or propositions. The art is of course to design a language that combines perspicuity and low complexity with reasonable expressive power. In this paper, we take a particularly simple approach. As preferences are binary relations between worlds, they naturally support standard unary modalities. In particular, our key modality ♦ϕ will just say that is ϕ true in some world which is at least as good as the current one. Of course, this notion can also be indexed to separate agents. The essence of this language is already in [4], but our semantics is more general, and so are our applications and later language extensions. Our modal language can express a variety of preference notions between propositions. Moreover, as already suggested in [9], it can “deconstruct” standard conditionals, providing an embedding of conditional logic into more standard modal logics. Next, we take the language to the analysis of games, where some sort of preference logic is evidently needed ([23] has a binary modal analysis different from ours). We show how a qualitative unary preference modality suffices for defining Nash Equilibrium in strategic games, and also the Backward Induction solution for finite extensive games. Finally, from a technical perspective, our treatment adds a new twist. Each application considered in this paper suggests the need for some additional access to worlds before the preference modality can unfold its true power.. (shrink)

A new possible world semantics for deontic logic is proposed. Its intuitive basis is that prohibitive predicates (such as "wrong" and "prohibited") have the property of negativity, i.e. that what is worse than something wrong is itself wrong. The logic of prohibitive predicates is built on this property and on preference logic. Prescriptive predicates are defined in terms of prohibitive predicates, according to the wellknown formula "ought" = "wrong that not". In this preference-based deontic (...) class='Hi'>logic (PDL), those theorems that give rise to the paradoxes of standard deontic logic (SDL) are not obtained. (E.g., O(p & q) → Op & Oq and Op → O(p v q)) are theorems of SDL but not of PDL.) The more plausible theorems of SDL, however, can be derived in PDL. (shrink)

Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study (...) the foundational issue of entanglement between preference and beliefs, and relate the resulting richer logics to belief revision theory and decision theory. (shrink)

If an agent prefers one kind of agents to the other agents, then the agent has first-order preferences. If the agent prefers agents with one kind of preferences to the other agents, then the agent has second-order preferences. The article proposes a sound, complete, and decidable logical system capable of expressing higher-order preferences.

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands ?upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or ?regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with (...) preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical ?utility update'. (shrink)

This thesis investigates two main issues concerning the behavior of rational agents, preference dynamics and agent diversity. -/- We take up two questions left aside by von Wright, and later also the multitude of his successors, in his seminal book Logic of Preference in 1963: reasons for preference, and changes in preference. Various notions of preference are discussed, compared and further correlated in the thesis. In particular, we concentrate on extrinsic preference. Contrary to (...) intrinsic preference, extrinsic preference is reason-based, i.e. one's preference for one option over another has a reason. A logical model is proposed and its properties are determined. Dynamics come in naturally, since reasons for the preferences can change. Logical systems and formal results regarding dynamical preference change are then presented. -/- Preference arises from comparisons between alternatives. A first option is to compare situations. Abstractly speaking, preferences are in this case between propositions, viewed as sets of possible worlds. The reasons can then be based on a `betterness' relation over possible worlds. Propositional preference arises as a lift from this primitive relation. A standard modal logical approach is taken and we use a modality for the betterness relation in the language. We then model preference change by techniques from dynamic epistemic logic (DEL), where a typical action, e.g. a suggestion or a command can change the betterness ordering of the worlds, and thereby the propositional preference. Dynamic reduction axioms are obtained to encode exactly how such a change takes place. We obtain a complete dynamic preference logic. -/- A second option is to compare objects as such. Concretely, properties of the objects often determine the preference over the objects. Properties are now the reasons. Inspired by Optimality Theory (OT), we propose a priority sequence, an ordering of properties. Various ways of getting a preference from the priority sequence are investigated, though we mostly follow the OT approach. We use a fragment of first-order logic to describe the situation. Here, on the dynamic side, it is priority change that leads to preference change. Using the DEL methodology again we propose a complete set of reduction axioms concerning the possible dynamic operations on priority sequences. -/- Not surprisingly, the above two views are closely related. After all, possible worlds can be thought of as objects! On the basis of a systematic comparison of the two views, we develop a two level perspective, in which the models themselves are structured in layers. In particular, correspondence results between the changes at the level of the possible worlds and the changes at the level of the priority sequences are proved. We end up by sketching a two-level preferential predicate logic to describe more complex circumstances in which situations and objects are compared simultaneously. -/- But we do not see this as the whole story. Preference does not live by itself, it is often intermingled with epistemic notions of knowledge and belief. One can have different intuitions about how this entanglement operates. A few options are discussed, and proposals for logical models are presented. When moving to dynamics, we now see a picture of knowledge update, belief revision and preference change taking place symbiotically, often unconsciously as in real life. -/- The resulting picture in the thesis is one of agents that process information and adjust beliefs and preferences in many different ways. There is no logically prescribed unique norm for doing this. The second part of the thesis takes this general phenomenon of diversity of agents as its focus, since it raises many issues for logical systems and the idealized agents which they normally presuppose. In reality, agents can differ across a wide spectrum of cognitive abilities and habits: in their memory capacity, observation power, inferential power, introspective ability, and revision policies when facing new information. -/- Two kinds of agents, perfect recall agents, and memory-free agents are studied thoroughly, in the setting of playing games. We show how current dynamic logics can be `parametrized' to allow for this memory diversity, with new characterizations of agent types resulting in complete dynamic-epistemic logics. The other dimension of the reality of diverse agents is that, however different they are, they often do manage to coordinate with each other successfully. While this theme has been prominent in game theory and multi-agent systems, it has received hardly any attention in logic. We analyze this interaction between different agents by looking at concrete scenarios which model their types explicitly. -/- Finally, we analyze the issue of agent diversity in its generality, discussing what dynamic logics would have to look like to become a full-fledged account of agents of different capacities and tendencies that pursue and sometimes achieve their goals in irreducibly social settings. -/- . (shrink)

The Barth–Krabbe–Hintikka–Hintikka Problem, independently raised by Barth and Krabbe and Hintikka and Hintikka Sherlock Holmes confronts modern logic: Toward a theory of information-seeking through questioning. Indiana University Press, Bloomington, 1983), is the problem of characterizing the strategic reasoning of the players of dialogical logic and game-theoretic semantics games from rational preferences rather than rules. We solve the problem by providing a set of preferences for players with bounded rationality and specifying strategic inferences from those preferences, for a variant (...) of logical dialogues. This solution is generalized to both game-theoretic semantics and orthodox dialogical logic. (shrink)

In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary acts as acts having mere conventional effects and perlocutionary acts as (...) acts having real effects upon attitudes and actions of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering so-called “deontic explosion”. (shrink)

In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete (...) axiomatisation for this class, without having the number of individuals or alternatives specified in the language. We are able to express classical axiomatic requirements in our first-order language, giving formal axioms for three classical theorems of preference aggregation by Arrow, by Sen, and by Kirman and Sondermann. We explore to what extent such theorems can be formally derived from our axiomatisations, obtaining positive results for Sen’s Theorem and the Kirman-Sondermann Theorem. For the case of Arrow’s Theorem, which does not apply in the case of infinite societies, we have to resort to fixing the number of individuals with an additional axiom. In the long run, we hope that our approach to formalisation can serve as the basis for a fully automated proof of classical and new theorems in social choice theory. (shrink)

The notion of preference is important in philosophy, decision theory, and many other disciplines. It is the interplay of information and preferences that provides the driving force behind what we actually do. The chapter adds a new focus and argues that preference is not static, instead, it changes dynamically when triggered by various kinds of events. We show that how a wide variety of preference changes can be modeled in logic, thereby providing the formal philosopher with (...) a natural extension of the scope of inquiry in the area of preference. (shrink)

The article studies preferences of agents in a setting with imperfect information. For such a setting, the authors propose a new class of preferences. It is said that an agent prefers one statement over another if, among all indistinguishable worlds, the agent prefers the worlds where the first statement is true to those where the second one is true. The main technical result is a sound and complete logical system describing the interplay between a binary modality capturing preferences and the (...) knowledge modality. The proof of completeness is using a newly proposed “tumbled pairs” technique. (shrink)

In the last few years, preference logic and in particular, the dynamic logic of preference change, has suddenly become a live topic in my Amsterdam and Stanford environments. At the request of the editors, this article explains how this interest came about, and what is happening. I mainly present a story around some recent dissertations and supporting papers, which are found in the references. There is no pretense at complete coverage of preference logic (for (...) that, see Hanson 2001) or even of preference change (Hanson 1995). (shrink)

In this paper I generalize the new approach to nonmonotonicreasoning that was presented in [6]. This generalization results in the inconsistency-adaptive logic PRL . I give proof theory, semantics, mention interesting properties,and comment on the reconstruction and amelioration of other nonmonotoniclogics and mechanisms.

Without introducing quantifiers, minimal axiomatic systems have already been constructed for Peirce's triadic logics. The present paper constructs a dual pair of axiomatic systems which can be used to introduce quantifiers into Peirce's preferred system of triadic logic. It is assumed (on the basis of textual evidence) that Peirce would prefer a system which rejects the absurd but tolerates the absolutely undecidable. The systems which are introduced are shown to be absolutely consistent, deductively complete, and minimal. These dual axiomatic (...) systems reveal an interesting elegance, independent of their historical motivation. (shrink)

This article demonstrates that typical restrictions which are imposed in dialogical logic in order to recover first-order logical consequence from a fragment of natural language argumentation are also forthcoming from preference profiles of boundedly rational players, provided that these players instantiate a specific player type and compute partial strategies. We present two structural rules, which are formulated similarly to closure rules for tableaux proofs that restrict players' strategies to a mapping between games in extensive forms and proof trees. (...) Both rules are motivated from players' preferences and limitations; they can therefore be viewed as being player-self-imposable. First-order logical consequence is thus shown to result from playing a specific type of argumentation game. The alignment of such games with the normative model of the Pragma-dialectical theory of argumentation is positively evaluated. But explicit rules to guarantee that the argumentation game instantiates first-order logical consequence have now become gratuitous, since their normative content arises directly from players' preferences and limitations. A similar naturalization for non-classical logics is discussed. (shrink)

An explication of preference and equivalence with regard to the evaluation of states of affairs. The logical system developed consists of the ordinary propositional calculus together with connectives standing for the notions above. In the course of this study a number of useful distinctions and definitions can be found. The author indicates that his logic of preference may be of use in connection with utility and decision theory, but does not develop this point.--R. H. T.

We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the (...) acyclicity axiom is not finitely axiomatizable in first-order logic. (shrink)

SOCREAL 2013 : 3rd International Workshop on Philosophy and Ethics of Social Reality 2013. Hokkaido University, Sapporo, Japan, 25-27 October 2013. Session 3 : Logic, Norms, and Preferences.

Our preferences determine how we act and think, but exactly what the mechanics are and how they work is a central cause of concern in many disciplines. This book uses techniques from modern logics of information flow and action to develop a unified new theory of what preference is and how it changes. The theory emphasizes reasons for preference, as well as its entanglement with our beliefs. Moreover, the book provides dynamic logical systems which describe the explicit triggers (...) driving preference change, including new information, suggestions, and commands. In sum, the book creates new bridges between many fields, from philosophy and computer science to economics, linguistics, and psychology. For the experienced scholar access to a large body of recent literature is provided and the novice gets a thorough introduction to the action and techniques of dynamic logic. (shrink)