Related papers: Scavenger 0.1: A Theorem Prover Based on Conflict …
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
Understanding and analyzing markets is crucial, yet analytical equilibrium solutions remain largely infeasible. Recent breakthroughs in equilibrium computation rely on zeroth-order policy gradient estimation. These approaches commonly…
The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…
This paper presents an up-to-date and refined version of the SCL calculus for first-order logic without equality. The refinement mainly consists of the following two parts: First, we incorporate a stronger notion of regularity into…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
In this work, we present a logic based on first-order CTL, namely Game Analysis Logic (GAL), in order to reason about games. We relate models and solution concepts of Game Theory as models and formulas of GAL, respectively. Precisely, we…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
Conflict-Based Search (CBS) is a state-of-the-art algorithm for multi-agent path finding. At the high level, CBS repeatedly detects conflicts and resolves one of them by splitting the current problem into two subproblems. Previous work…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the…
Progression, the task of updating a knowledge base to reflect action effects, generally requires second-order logic. Identifying first-order special cases, by restricting either the knowledge base or action effects, has long been a central…
We present 1-Pager the first system that answers a question and retrieves evidence using a single Transformer-based model and decoding process. 1-Pager incrementally partitions the retrieval corpus using constrained decoding to select a…
Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify…
Our ability to know when to trust the decisions made by machine learning systems has not kept up with the staggering improvements in their performance, limiting their applicability in high-stakes domains. We introduce Prover-Verifier Games…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
Tackling Natural Language Inference with a logic-based method is becoming less and less common. While this might have been counterintuitive several decades ago, nowadays it seems pretty obvious. The main reasons for such a conception are…