Epistemic attack semantics

We present a probabilistic interpretation of the plausibility of attacks in abstract argumentation frameworks by extending the epistemic approach to probabilistic argumentation with probabilities on attacks. By doing so we also generalise the previously proposed attack semantics by Villata et al. to the probabilistic setting and provide a fine-grained assessment of the plausibility of attacks. We also consider the setting where partial probabilistic information on arguments and/or attacks is given and missing probabilities have to be derived

Epistemic attack semantics

We present a probabilistic interpretation of the plausibility of attacks in abstract argumentation frameworks by extending the epistemic approach to probabilistic argumentation with probabilities on attacks. By doing so we also generalise the previously proposed attack semantics by Villata et al. to the probabilistic setting and provide a fine-grained assessment of the plausibility of attacks. We also consider the setting where partial probabilistic information on arguments and/or attacks is given and missing probabilities have to be derived

A Labelling Framework for Probabilistic Argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature

Empirical Evaluation of Abstract Argumentation: Supporting the Need for Bipolar and Probabilistic Approaches

In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted, rejected, undecided), adjust their views when new and correct information comes in, and that a framework handling only attack relations is sufficient to represent their opinions. Although it is natural to make these assumptions as a starting point for further research, removing them or even acknowledging that such removal should happen is more challenging for some of these concepts than for others. Probabilistic argumentation is one of the approaches that can be harnessed for more accurate user modelling. The epistemic approach allows us to represent how much a given argument is believed by a given person, offering us the possibility to express more than just three agreement states. It is equipped with a wide range of postulates, including those that do not make any restrictions concerning how initial arguments should be viewed, thus potentially being more adequate for handling beliefs of the people that have not fully disclosed their opinions in comparison to Dung's semantics. The constellation approach can be used to represent the views of different people concerning the structure of the framework we are dealing with, including cases in which not all relations are acknowledged or when they are seen differently than intended. Finally, bipolar argumentation frameworks can be used to express both positive and negative relations between arguments. In this paper we describe the results of an experiment in which participants judged dialogues in terms of agreement and structure. We compare our findings with the aforementioned assumptions as well as with the constellation and epistemic approaches to probabilistic argumentation and bipolar argumentation

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Probabilistic Argumentation with Epistemic Extensions and Incomplete Information

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed to this assignment. In this paper, we regard the assignment as denoting the belief that an agent has that an argument is justifiable, i.e., that both the premises of the argument and the derivation of the claim of the argument from its premises are valid. This leads to the notion of an epistemic extension which is the subset of the arguments in the graph that are believed to some degree (which we defined as the arguments that have a probability assignment greater than 0.5). We consider various constraints on the probability assignment. Some constraints correspond to standard notions of extensions, such as grounded or stable extensions, and some constraints give us new kinds of extensions

The Logic of Joint Ability in Two-Player Tacit Games

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality

Classical Knowledge for Quantum Security

We propose a decision procedure for analysing security of quantum cryptographic protocols, combining a classical algebraic rewrite system for knowledge with an operational semantics for quantum distributed computing. As a test case, we use our procedure to reason about security properties of a recently developed quantum secret sharing protocol that uses graph states. We analyze three different scenarios based on the safety assumptions of the classical and quantum channels and discover the path of an attack in the presence of an adversary. The epistemic analysis that leads to this and similar types of attacks is purely based on our classical notion of knowledge.Comment: extended abstract, 13 page

Explicit Evidence Systems with Common Knowledge

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic