Sjur Dyrkolbotn

Propositional discourse logic

A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: non-paradoxical character of discourses, admissibility of arguments in argumentation networks, propositional satisfiability, and the existence of kernels of directed graphs. Directed graphs provide the basis for the semantics of pdl and the paper concludes by an overview of relevant graph-theoretical results and their applications in diagnosing paradoxical character of natural discourses.

Finding kernels or solving SAT

We begin by offering a new, direct proof of the equivalence between the problem of the existence of kernels in digraphs, KER, and satisfiability of propositional theories, SAT, giving linear reductions in both directions. Having introduced some linear reductions of the input graph, we present new algorithms for KER, with variations utilizing solvers of boolean equations. In the worst case, the algorithms try all assignments to either a feedback vertex set, F, or a set of nodes E touching only all even cycles. Hence KER is fixed parameter tractable not only in the size of F, as observed earlier, but also in the size of E. A slight modification of these algorithms leads to a branch and bound algorithm for KER which is virtually identical to the DPLL algorithm for SAT. This suggests deeper analogies between the two problems and the probable scenario of KER research facing the challenges known from the work on SAT. The algorithm gives also the upper bound O^@?(1.427^|^G^|) on the time complexity of general KER and O^@?(1.286^|^G^|) of KER for oriented graphs, where |G| is the number of vertices.

The Same, Similar, or Just Completely Different? Equivalence for Argumentation in Light of Logic

In recent years, argumentation theory and logic have moved closer to each other, a development due in large part to Dungs mathematically precise definition of an abstract argumentation framework as a digraph and the intuitively plausible semantics for argumentation that can be formulated using this structure. This work raises some questions, however, regarding the relationship between an abstract argumentation framework --- a directed graph --- and the underlying argumentative structure that it is taken to represent. One such question, which we study in this paper, is the question of when two arguments should be considered the same, a question which has been surprisingly controversial, and which also, as we will demonstrate, gives rise to interesting technical results and future challenges.

Agents Homogeneous: A Procedurally Anonymous Semantics Characterizing the Homogeneous Fragment of ATL

In many multi-agent scenarios we encounter homogeneous groups of agents; agents that have the same actions available, and for which the system does not care who performs a given action, but only cares about how many agents perform it. Sometimes homogeneity is a descriptive fact, arising from a lack of interest in agents’ identity, or the fact that we are simply unable to distinguish between them. Other times, it is a normative requirement, for instance in the context of voting, where we do not want the outcome to depend on who voted for what, only on how many votes each candidate receives. Another important notion is anonymity, which also often arise in multi-agent scenarios, either because we do not know an agent’s identity, or else because the systems comes with an explicit commitment to ensure that this information is kept secret. Clearly, the two notions are closely related, and in this paper we explore the relationship that exists between them within the framework of Alternating-time Temporal Logic. We add an homogeneity axiom to this logic, and proceed to show that the resulting logic, which we dub hatl, is sound and complete with respect to a class of structures that are both homogeneous and procedurally anonymous, meaning that no information whatsoever needs to be maintained about the actions of individual agents.

Reasoning about reasons behind preferences using modal logic

Preferences play a crucial role in the theory of rationality, and therefore also to computational social choice and artificial intelligence. In formal models it is usually assumed that preferences are primitive objects, and little concern is devoted to the question of how they are formed or where they come from. Recent work in rational choice theory challenges this assumption, however, and aims to give more internal structure to the notion of a preference. The focus so far has been on modeling faculties of individual agents, such as their mood, mindset, and motivating reasons. In this paper we contribute to this development by developing a modal logic for reasoning about preferences that depend on a set of motivationally salient properties. The main result is a translation showing how reasoning in this logic can be captured by reasoning in a standard modal logic (KT with universal modality). It follows that reasoning systems and algorithms developed for modal logic (with universal modality) can be employed for reasoning about reason-based preferences. We then discuss how the approach can be generalised to the multi-agent case, and allows us to reason about agents who disagree because they are motivated by different factors, and who might be able to reach consensus simply by changing their perspective.

Concurrent Game Structures with Roles

In the following paper we present a new semantics for the well-known strategic logic ATL. It is based on adding roles to concurrent game structures, that is at every state, each agent belongs to exactly one role, and the role specifies what actions are available to him at that state. We show advantages of the new semantics, provide motivating examples based on sensor networks, and analyze model checking complexity.

On a Formal Connection between Truth, Argumentation and Belief

Building on recent connections established between formal models used to study truth and argumentation, we define logics for reasoning about them that we then go on to axiomatize, relying on a link with three-valued Eukasiewicz logic. The first set of logics we introduce are based on formalizing so called skep- tical reasoning, and our result shows that a range of semantics that are distinct for particular models coincide at the level of validities. Then, responding to the challenge that our logics do not capture credulous reasoning, we explore modal extensions, leading us to introduce models of three-valued belief induced by ar- gument. We go on to take a preliminary look at some formal properties of this framework, offer a conjecture, then conclude by presenting some challenges for future work.

Reasonably rational: reasoning about reasons behind preferences using modal logic

Reasoning about preferences is a fundamental component of rationality, and therefore central in AI and computational social choice. Most logic-based frameworks for representing and reasoning about preferences assume that preferences are arbitrarily given, typically as a ranking of a set of alternatives or using utilities, with little concern about how preferences are formed or where they come from. Recent work in rational choice theory, however, has devoted attention to giving more internal structure to the notion of rationality, focusing more on the faculties of individual agents, such as their mood, mindset, and motivating reasons. In this paper we develop a modal logic for reasoning about preferences that depend on a set of motivationally salient properties, based on recent work on reasons behind preferences by Dietrich and List. The main result is that we show how the problem of reasoning in this logic can be translated to reasoning in a standard modal logic (KT with universal modality), and consequently that reasoning systems and algorithms developed for modal logic (with universal modality) can be employed for reasoning about reason-based preferences.

Kernels in digraphs that are not kernel perfect

Abstract An equivalent of kernel existence is formulated using semikernels. It facilitates inductive arguments, which allow us to establish several sufficient conditions for the existence of kernels in finite digraphs. The conditions identify classes of digraphs that have kernels without necessarily being kernel perfect.

A Typology of Liability Rules for Robot Harms

This paper considers non-contractual liability for harms caused by (artificially) intelligent systems. It provides a typology of different ways to approach the liability issue, exemplified by some new technologies that have been, or are about to be, introduced into human society. The paper argues that the traditional robot-as-tool perspective should be maintained, but warns that this might not be possible unless we develop corresponding technologies for efficient responsibility tracking. Specifically, new techniques need to be developed, at the intersection between computer science and law, to support reasoning about the liability implications when autonomous technologies interact with their environment and cause harms.