Related papers: A Game for Counting Logic Formula Size and an Appl…
Let \phi be a first order formula and M be a countable model. \phi^M denotes the set of all assignments that satisfy \phi in M. Let M, N be countable models. A formula \phi distinguishes these models if |\phi^M|\neq |\phi^N|. We show that…
First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…
Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large…
The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a…
We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
We introduce the framework of LLM-Stackelberg games, a class of sequential decision-making models that integrate large language models (LLMs) into strategic interactions between a leader and a follower. Departing from classical Stackelberg…
We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the…
In applied game theory the motivation of players is a key element. It is encoded in the payoffs of the game form and often based on utility functions. But there are cases were formal descriptions in the form of a utility function do not…
In this work we investigate the computational complexity of the satisfiability problem of sub-fragments of the Bernays-Schoenfinkel class of first-order logic, also known as EPR (Effectively Propositional). While Bernays-Schoenfinkel is…
We focus on the problem of \emph{Answer-Level Fine-Tuning} (ALFT), where the goal is to optimize a language model based on the correctness or properties of its final answers, rather than the specific reasoning traces used to produce them.…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
We study rational agents with different perception capabilities in strategic games. We focus on a class of one-shot limited-perception games. These games extend simultaneous-move normal-form games by presenting each player with an…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…
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…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…
{\AA}qvist's logics (E, F, F+(CM), and G) are among the best-known systems in the long tradition of preference-based approaches for modeling conditional obligation. While the general semantics of preference models align well with…
We introduce a generalization of the bisimulation game that finds distinguishing Hennessy-Milner logic formulas from every finitary, subformula-closed language in van Glabbeek's linear-time--branching-time spectrum between two finite-state…
Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…
Large Language Models (LLMs) have demonstrated notable capabilities across various tasks, showcasing complex problem-solving abilities. Understanding and executing complex rules, along with multi-step planning, are fundamental to logical…