We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...) is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and Chellas’s STIT. (shrink)

Many aspects of how humans form and combine concepts are notoriously difficult to capture formally. In this paper, we focus on the representation of three particular such aspects, namely overexten- sion, underextension, and dominance. Inspired in part by the work of Hampton, we consider concepts as given through a prototype view, and by considering the interdependencies between the attributes that define a concept. To approach this formally, we employ a recently introduced family of operators that enrich Description Logic languages. These (...) operators aim to characterise complex concepts by collecting those instances that apply, in a finely controlled way, to ‘enough’ of the concept’s defin- ing attributes. Here, the meaning of ‘enough’ is technically realised by accumulating weights of satisfied attributes and comparing with a given threshold that needs to be met. (shrink)

We introduce a family of operators to combine Description Logic concepts. They aim to characterise complex concepts that apply to instances that satisfy \enough" of the concept descriptions given. For instance, an individual might not have any tusks, but still be considered an elephant. To formalise the meaning of "enough", the operators take a list of weighted concepts as arguments, and a certain threshold to be met. We commence a study of the formal properties of these operators, and study some (...) variations. The intended applications concern the representation of cognitive aspects of classi cation tasks: the interdependencies among the attributes that de ne a concept, the prototype of a concept, and the typicality of the instances. (shrink)

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting (...) attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation. (shrink)

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that', and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu. We start by recalling a simplification of the Ldm that has been proposed in previous (...) work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL. (shrink)

We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment needed for their formalization, and (...) even simplify their logical formulation. (shrink)

We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a logic of agency. (...) In particular, we apply it to reason about the resource-sensitive use of artefacts. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a (...) complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a (...) complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

Information about the powers and abilities of acting entities is used to coordinate their actions in societies, either physical or digital. Yet, the commonsensical meaning of an acting entity being deemed able to do something is still missing from the existing specification languages for the web or for multi-agent systems. We advance a general purpose abstract logical account of evidence-based ability. A basic model can be thought of as the ongoing trace of a multi-agent system. Every state records systemic confirmations (...) and disconfirmations of whether an acting entity is able to bring about something. Qualitative inductive reasoning is then used in order to infer what acting entities are deemed able to bring about in the multi-agent system. A temporalised modal language is used to talk about deemed ability, actual agency, and confirmation and disconfirmation of deemed ability. What constitutes a confirmation and a disconfirmation is left to the modeller as in general it depends on the application at hand. So to illustrate the methodology we propose two extended examples, one in practical philosophy, the other in system engineering. We first use a logic of agency and ability to obtain a version of Mele’s general practical abilities. Then, we look at the management of abilities in a supervised system. (shrink)