相关论文: Boole's Chapter XV: Syllogism Details

Logics for reasoning about knowledge and actions have seen many applications in various domains of multi-agent systems, including epistemic planning. Change of knowledge based on observations about the surroundings forms a key aspect in…

The historiography of logic conceives of a Fregean revolution in which modern mathematical logic (also called symbolic logic) has replaced Aristotelian logic. The preeminent expositors of this conception are Jean van Heijenoort (1912-1986)…

This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…

Although randomization has long been used in distributed computing, formal methods for reasoning about probabilistic concurrent programs have lagged behind. No existing program logics can express specifications about the full distributions…

The laws of quantum mechanics are couched in subtle mathematical language. The laws are not usually stated in a compact pedagogical form. Here I present a possible way to correct this. Essential facts can be distilled into seven statements…

We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…

We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on justification terms and equality predicate on terms. In…

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper…

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…

The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…

This paper discusses a forgotten remark of Paul L\'evy (1935), determining the asymptotic distribution of sums of i.i.d. random variables with tails $cx^{-\alpha}\psi(\log x)$, where $0<\alpha<2$ and $\psi$ is a periodic function on…

This paper undertakes a re-examination of Sir William Hamilton's doctrine of the quantification of the predicate. Hamilton's doctrine comprises two theses. First, the predicates of traditional syllogistic sentence-forms contain implicit…

Let S be a set of states of a physical system and p(s) the probability of the occurrence of an event when the system is in state s. A function p from S to [0,1] is called a numerical event or alternatively, an S-probability. If a set P of…

Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…

This monograph is an account of the theory of fallible probability and of the dynamics of degrees of belief. It discusses the first order subjective theory in which first order degrees of belief are expressed by subjective probabilities and…

Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…