Related papers: Relative Entailment Among Probabilistic Implicatio…
We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…
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…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…
Do LMs infer the semantics of text from co-occurrence patterns in their training data? Merrill et al. (2022) argue that, in theory, sentence co-occurrence probabilities predicted by an optimal LM should reflect the entailment relationship…
A nonmonotonic logic of thresholded generalizations is presented. Given propositions A and B from a language L and a positive integer k, the thresholded generalization A=>B{k} means that the conditional probability P(B|A) falls short of one…
We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment…
We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's…
Deep learning techniques are increasingly popular in the textual entailment task, overcoming the fragility of traditional discrete models with hard alignments and logics. In particular, the recently proposed attention models (Rockt\"aschel…
We evaluate LLMs' language understanding capacities on simple inference tasks that most humans find trivial. Specifically, we target (i) grammatically-specified entailments, (ii) premises with evidential adverbs of uncertainty, and (iii)…
We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point…
Textual entailment recognition is one of the basic natural language understanding(NLU) tasks. Understanding the meaning of sentences is a prerequisite before applying any natural language processing(NLP) techniques to automatically…
Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
We define a novel textual entailment task that requires inference over multiple premise sentences. We present a new dataset for this task that minimizes trivial lexical inferences, emphasizes knowledge of everyday events, and presents a…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of…
Association Rules are a basic concept of data mining. They are, however, not understood as logical objects which can be used for reasoning. The purpose of this paper is to investigate a model based semantic for implications with certain…