Related papers: Probabilistic Default Reasoning with Conditional C…
Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears…
The constraints proposed recently by Bershadsky to produce $W^l_n$ algebras are a mixture of first and second class constraints and are degenerate. We show that they admit a first-class subsystem from which they can be recovered by…
Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal…
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…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…
We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
Neglecting many motivating details for the Park-Pham theorem (previously known as the Kahn-Kalai conjecture), the result starts with a finite set $X$, a non-trivial upper set $\mathcal{F} \subseteq 2^X$, and a particular parameterized…
We introduce isotonic conditional laws (ICL) which extend the classical notion of conditional laws by the additional requirement that there exists an isotonic relationship between the random variable of interest and the conditioning random…
Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically…
This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of…
Pearl's front-door criterion provides a set of sufficient conditions for estimating the total causal effect from observational data in the presence of latent confounding, using the functional P(y | do(x := x*)) = \sum_z P(z | x*) \sum_x P(y…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
A serious defect with the Halpern-Pearl (HP) definition of causality is repaired by combining a theory of causality with a theory of defaults. In addition, it is shown that (despite a claim to the contrary) a cause according to the HP…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated…
Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…