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We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to…
Model-checking HyperLTL, a temporal logic expressing properties of sets of traces with applications to information-flow based security and privacy, has a decidable, but TOWER-complete, model-checking problem. While the classical…
We use a category-theoretic formulation of Aczel's Fullness Axiom from Constructive Set Theory to derive the local cartesian closure of an exact completion. As an application, we prove that such a formulation is valid in the homotopy…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not…
(CROPPED TO FIT IN ARXIV'S SILLY LIMIT. SEE PDF FOR COMPLETE ABSTRACT.) We are the first to thoroughly explore a large space of formal secure compilation criteria based on robust property preservation, i.e., the preservation of properties…
We prove The Equivalence Theorem: structurally complete knowledge representation requires exactly four mutually entailing capabilities -- n-ary relationships with attributes, temporal validity, uncertainty quantification, and causal…
This article presents a formalism inspired by Dennett's notion of the intentional stance. Whereas Dennett's treatment of these concepts is informal, we aim to provide a more formal analogue. We introduce a framework based on stochastic…
In a strand of the literature, it is assumed that the common prior has full support; that is, every type of every player is assigned positive probability. Morris (1991,1994) established an epistemological-behavioral duality characterisation…
We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
This paper describes a process for constructing situation-specific belief networks from a knowledge base of network fragments. A situation-specific network is a minimal query complete network constructed from a knowledge base in response to…
We propose a general definition of perfect equilibrium which is applicable to a wide class of games. A key feature is the concept of completely mixed nets of strategies, based on a more detailed notion of carrier of a strategy. Under…
In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is…
We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
We introduce and investigate here a formalisation for conditionals that allows the definition of a broad class of reasoning systems. This framework covers the most popular kinds of conditional reasoning in logic-based KR: the semantics we…