Related papers: Predicate Exchangeability and Language Invariance …
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.…
The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…
Grammaticality and likelihood are distinct notions in human language. Pretrained language models (LMs), which are probabilistic models of language fitted to maximize corpus likelihood, generate grammatically well-formed text and…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language. This so-called $W$-index allows for naming arbitrary computably enumerable languages, with the drawback that even the membership…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
We consider prescriptive type systems for logic programs (as in Goedel or Mercury). In such systems, the typing is static, but it guarantees an operational property: if a program is "well-typed", then all derivations starting in a…
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…
We analyse preference inference, through consistency, for general preference languages based on lexicographic models. We identify a property, which we call strong compositionality, that applies for many natural kinds of preference…
Recent investigations into the inner-workings of state-of-the-art large-scale pre-trained Transformer-based Natural Language Understanding (NLU) models indicate that they appear to know humanlike syntax, at least to some extent. We provide…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
Exchangeability -- in which the distribution of an infinite sequence is invariant to reorderings of its elements -- implies the existence of a simple conditional independence structure that may be leveraged in the design of statistical…
Meanings of words change over time and across domains. Detecting the semantic changes of words is an important task for various NLP applications that must make time-sensitive predictions. We consider the problem of predicting whether a…
Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…