Related papers: Probabilities on Sentences in an Expressive Logic
A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the…
Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…
In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can…
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…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…