Related papers: Logic, Probability and Action: A Situation Calculu…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension…
The interest in the combination of probability with logics for modeling the world has rapidly increased in the last few years. One of the most effective approaches is the Distribution Semantics which was adopted by many logic programming…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
In Probabilistic Logic Nilsson uses the device of a probability distribution over a set of possible worlds to assign probabilities to the sentences of a logical language. In his paper Nilsson concentrated on inference and associated…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
Over the last decade, the use of robots in production and daily life has increased. With increasingly complex tasks and interaction in different environments including humans, robots are required a higher level of autonomy for efficient…
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…
With the increasing interest in using large language models (LLMs) for planning in natural language, understanding their behaviors becomes an important research question. This work conducts a systematic investigation of LLMs' ability to…
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…
Recent advances in AI have been significantly driven by the capabilities of large language models (LLMs) to solve complex problems in ways that resemble human thinking. However, there is an ongoing debate about the extent to which LLMs are…
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…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and…
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…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
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…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…