Related papers: Complete Conditional Type Structures
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…
We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory. The key concept we employ is that of a Lawvere…
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of…
For an arbitrary category, we consider the least class of functors con- taining the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
Traditionally, Epistemic Logic represents epistemic scenarios using a single model. This, however, covers only complete descriptions that specify truth values of all assertions. Indeed, many -- and perhaps most -- epistemic descriptions are…
We define a modification of the standard Kripke model, called the ordered Kripke model, by introducing a linear order on the set of accessible states of each state. We first show this model can be used to describe the lexicographic belief…
The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we…
We provide a novel semantics for belief using simplicial complexes. In our framework, belief satisfies the \textsf{KD45} axioms and rules as well as the ``knowledge implies belief'' axiom ($K\phi \lthen B\phi$); in addition, we adopt the…
A notion of central importance in categorical topology is that of topological functor. A faithful functor E -> B is called topological if it admits cartesian liftings of all (possibly large) families of arrows; the basic example is the…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
Any strategy and prior probability together are a coherent conditional probability that can be extended, generally not in a unique way, to a full conditional probability. The corresponding class of extensions is studied and a closed form…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
A description is an entity that can be interpreted as true or false of an object, and using feature structures as descriptions accrues several computational benefits. In this paper, I create an explicit interpretation of a typed feature…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
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…