Authors:Piotr Kulicki; Robert Trypuz, Robert Craven, Marek J. Sergot Abstract: This paper studies some normative relations that hold between actions, their preconditions and their effects, with particular attention to connecting what are often called ‘ought to be’ norms with ‘ought to do’ norms. We use a formal model based on a form of transition system called a ‘coloured labelled transition system’ (coloured LTS) introduced in a series of papers by Sergot and Craven. Those works have variously presented a formalism (an ‘action language’) nC+ for defining and computing with a (coloured) LTS, and another, separate formalism, a modal language interpreted on a (coloured) LTS used to express its properties. We consolidate these two strands. Instead of specifying the obligatory and prohibited states and transitions as part of the construction of a coloured LTS as in nC+, we represent norms in the modal language and use those to construct a coloured LTS from a given regular (uncoloured) one. We also show how connections between norms on states and norms on transitions previously treated as fixed constraints of a coloured LTS can instead be defined within the modal language used for representing norms. PubDate: Fri, 02 Jun 2023 00:00:00 +020
Authors:Nathaniel Gan Abstract: This paper examines several intended topological features of the Region Connection Calculus (RCC) and argues that they are either underdetermined by the formal theory or given by the complement axiom. Conditions are identified under which the axioms of RCC are satisfied in topological models under various set restrictions. The results generalise previous results in the literature to non-strict topological models and across possible interpretations of connection. It is shown that the intended interpretation of connection and the alignment of self-connection with topological connection are underdetermined by the axioms of RCC, which suggests that additional axioms are necessary to secure these features. It is also argued that the complement axiom gives RCC models much of their topological structure. In particular, the incompatibility of RCC with interiors is argued to be given by the complement axiom. PubDate: Thu, 06 Apr 2023 00:00:00 +020
Authors:Miloš Arsenijević; Andrej Jandrić Abstract: It is shown how the temporal-modal system of events TM (axiomatized in Appendix) allows for the avoidance of the logical determinism without the rejection of the principle of bivalence. The point is that the temporal and the modal parts of TM are so inter-related that modalities are in-the-real-world-inherent modalities independently of whether they concern actual or only possible events. Though formulated in a tenseless language, whose interpretation does not require the assumption of tense facts at the basic level of reality, TM implies an objective, observer-independent difference between tenses based only on the way in which modalities are distributed along the time continuum. The conclusion is that the arrow of time is an intra-model characteristic of any model of TM that describes the non-deterministic real world up to a certain point of its history, while the flow of time is an inter-model characteristic of the continuous transition between these models. PubDate: Mon, 27 Mar 2023 00:00:00 +020
Authors:Paolo Maffezioli Abstract: I provide a mereological analysis of Zeno of Sidon’s objection that in Euclid’s Elements we need to supplement the principle that there are no common segments of straight lines and circumferences. The objection is based on the claim that such a principle is presupposed in the proof that the diameter cuts the circle in half. Against Zeno, Posidonius attempts to prove the bisection of the circle without resorting to Zeno’s principle. I show that Posidonius’ proof is flawed as it fails to account for the case in which one of the two circumferences cut by the diameter is a proper part of the other. When such a case is considered, then either the bisection of the circle is false or it presupposes Zeno’s principle, as claimed by Zeno. PubDate: Thu, 24 Nov 2022 00:00:00 +010
Authors:Giuseppina Barbieri; Giangiacomo Gerla Abstract: We face with the question of a suitable measure theory in Euclidean point-free geometry and we sketch out some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the notion of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions. PubDate: Fri, 18 Nov 2022 00:00:00 +010
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