Related papers: Strength Factors: An Uncertainty System for a Quan…

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…

The decidability of a logical system refers to the existence of an algorithm that can determine whether any given formula in that system is a theorem. In this paper, Harrop's lemma is used to prove the decidability of quantum modal logic.

The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

In these notes we propose a new, simpler proof system for first-order matching logic with application and definedness. The new proof system is inspired by Tarski's axiomatization for first order-logic with equality (simplified by Kalish and…

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…

Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…

We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate strongly to quantitative probabilistic logics, and in fact the…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Defeasible statements are statements that are likely, or probable, or usually true, but may occasionally be false. Plausible reasoning makes conclusions from statements that are either facts or defeasible statements without using numbers.…

A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

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 the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal')…