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Can the large language models (LLMs) solve challenging first-order combinatorial reasoning problems such as graph coloring, knapsack, and cryptarithmetic? By first-order, we mean these problems can be instantiated with potentially an…

First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…

With the aim of improving performance in Markov Decision Problem in an Off-Policy setting, we suggest taking inspiration from what is done in Offline Reinforcement Learning (RL). In Offline RL, it is a common practice during policy learning…

Solving multi-objective optimization problems is important in various applications where users are interested in obtaining optimal policies subject to multiple, yet often conflicting objectives. A typical approach to obtain optimal policies…

The paper studies the highly prototypical Fictitious Play (FP) algorithm, as well as a broad class of learning processes based on best-response dynamics, that we refer to as FP-type algorithms. A well-known shortcoming of FP is that, while…

Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or…

Human beings are particularly good at reasoning and inference from just a few examples. When facing new tasks, humans will leverage knowledge and skills learned before, and quickly integrate them with the new task. In addition to learning…

We consider the problem of computing optimal generalised policies for relational Markov decision processes. We describe an approach combining some of the benefits of purely inductive techniques with those of symbolic dynamic programming…

Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…

Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…

Alloy is a well-known, formal, declarative language for modelling systems early in the software development process. Currently, it uses the Kodkod library as a back-end for finite model finding. Kodkod translates the model to a SAT problem;…

Recent years have witnessed significant advances in reinforcement learning (RL), which has registered great success in solving various sequential decision-making problems in machine learning. Most of the successful RL applications, e.g.,…

Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…

Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…

Recent advances in Reinforcement Learning (RL) largely benefit from the inclusion of Deep Neural Networks, boosting the number of novel approaches proposed in the field of Deep Reinforcement Learning (DRL). These techniques demonstrate the…

Game theory provides a mathematical way to study the interaction between multiple decision makers. However, classical game-theoretic analysis is limited in scalability due to the large number of strategies, precluding direct application to…

This paper addresses the longstanding problem of determining the structure of the $\leq_{\mathrm{LT}}$-order in the Effective Topos, known to effectively embed the Turing degrees. In a surprising discovery, we show that the…

We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our primary method employs a version of the double oracle, iteratively adding strategies…

We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…