Logic and Argumentation

While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group knowledge and belief under different assumptions about which properties knowledge and belief have. In particular, we map out (lack of) preservation of knowledge/belief properties against different standard definitions of group knowledge/belief. It turns out that what is called group belief most often is not actually belief, i.e., does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, distributed belief is not actually belief (it does not satisfy the D axiom). In the literature there is no detailed completeness proof for axiomatizations of KD45 with distributed belief that we are aware of, and there has been some confusion regarding soundness of such axiomatizations related to the mentioned lack of preservation. In this paper we also present a detailed completeness proof for a sound axiomatization of KD45 with distributed belief.

A methodology for the formalization of legal texts is presented. This methodology is based on features of the NAI Suite, a recently developed formalization environment for legal texts. The ability of the tool to execute queries is used in order to drive a correct formalization until all queries are validated. The approach is studied on a fragment of the Smoking Prohibition (Children in Motor Vehicles) (Scotland) Act 2016 of the Scottish Parliament.

In this paper we look at different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization, for which balance theory forms a network-theoretical underpinning. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this paper we examine different possibilities for extending this basic language, in order to, first, be able to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms, and, second, be able to define the property of full balance rather than balanced-up-to-a-degree. We consider extensions with both static modalities such as the universal and the difference modality, the intersection modality, and nominals known from hybrid logic, as well as dynamic global bridge modalities known from sabotage logic. Along the way we provide axioms for weak balance. Finally, to explore measures of how far a network is from polarization, we consider and compare variations of distance measures between models in relation to balance.