Related papers: Extending E Prover with Similarity Based Clause Se…

We describe several additions to the ENIGMA system that guides clause selection in the E automated theorem prover. First, we significantly speed up its neural guidance by adding server-based GPU evaluation. The second addition is motivated…

Selection strategies are broadly used in first-order logic theorem proving to select those parts of a large knowledge base that are necessary to proof a theorem at hand. Usually, these selection strategies do not take the meaning of symbol…

We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite…

Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are…

The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…

Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…

Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…

A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…

This paper examines the accuracy of the PROSPECTOR model for uncertain reasoning. PROSPECTOR's solutions for a large number of computer-generated inference networks were compared to those obtained from probability theory and minimum…

A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…

Probing classifiers have emerged as one of the prominent methodologies for interpreting and analyzing deep neural network models of natural language processing. The basic idea is simple -- a classifier is trained to predict some linguistic…

In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…

We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…

Sentence encoders map sentences to real valued vectors for use in downstream applications. To peek into these representations - e.g., to increase interpretability of their results - probing tasks have been designed which query them for…

Query expansion is a well known method to improve the performance of information retrieval systems. In this work we have tested different approaches to extract the candidate query terms from the top ranked documents returned by the…

Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…

Large language models increasingly rely on explicit reasoning chains and can produce multiple plausible responses for a given context. We study the candidate sampler that produces the set of plausible responses contrasting the ancestral…

We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from…

Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which…

We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…