Related papers: Probabilities are always axiomatizable
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…
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…
We prove completeness of preferential conditional logic with respect to convexity over finite sets of points in the Euclidean plane. A conditional is defined to be true in a finite set of points if all extreme points of the set interpreting…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
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…
Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…
There are multiple proposed interpretations of probability theory: one such interpretation is true-false logic under uncertainty. Cox's Theorem is a representation theorem that states, under a certain set of axioms describing the meaning of…
In a recent work Foulis and Pulmannov\' a \cite{Foulis2012} studied the logical connectives in lattice effect algebras. In this paper we extend their study and investigate further the logical calculus for which the lattice effect algebras…
We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are…
We study approximate equivalence relations up to commensurability, in the presence of a definable measure. As a basic framework, we give a presentation of probability logic based on continuous logic. Hoover's normal form is valid here; if…
Our concern is the axiomatisation problem for modal and algebraic logics that correspond to various fragments of two-variable first-order logic with counting quantifiers. In particular, we consider modal products with Diff, the…