Related papers: Proof Systems Based on Structured Circuits

The ability to reason under uncertainty and with incomplete information is a fundamental requirement of decision support technology. In this paper we argue that the concentration on theoretical techniques for the evaluation and selection of…

A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…

We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…

We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for…

This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories.…

The evaluation of a query over a probabilistic database boils down to computing the probability of a suitable Boolean function, the lineage of the query over the database. The method of query compilation approaches the task in two stages:…

First-Order Boolean Networks with Non-deterministic updates (FOBNN) compute a boolean transition graph representing the absence and presence of species over time. The utility of FOBNNs has been justified by their theoretical soundness with…

For safety assurance of deep neural networks (DNNs), out-of-distribution (OoD) monitoring techniques are essential as they filter spurious input that is distant from the training dataset. This paper studies the problem of systematically…

This paper presents a new compressed representation of Boolean functions, called CFLOBDDs (for Context-Free-Language Ordered Binary Decision Diagrams). They are essentially a plug-compatible alternative to BDDs (Binary Decision Diagrams),…

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…

Can models with particular structure avoid being biased towards spurious correlation in out-of-distribution (OOD) generalization? Peters et al. (2016) provides a positive answer for linear cases. In this paper, we use a functional modular…

The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the…

We present a logical system CFP (Concurrent Fixed Point Logic) supporting the extraction of nondeterministic and concurrent programs that are provably total and correct. CFP is an intuitionistic first-order logic with inductive and…

Since the introduction of the Ideal Proof System (IPS) by Grochow and Pitassi (J. ACM 2018), a substantial body of work has established size lower bounds for IPS and its fragments. In particular, Forbes, Shpilka, Tzameret, and Wigderson…

We explore the use of FCNNs (Fully Connected Neural Networks) for designing end-to-end communication systems without taking any inspiration from existing classical communications models or error control coding. This work relies solely on…

This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…

Neural Disjunctive Normal Form (DNF) based models are powerful and interpretable approaches to neuro-symbolic learning and have shown promising results in classification and reinforcement learning settings without prior knowledge of the…

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

We study the complexity of inverse cellular automata on configurations of bounded size. Deciding injectivity in this setting is co-NP-complete by a theorem of Durand. We give a simpler proof of this theorem by a direct reduction from UNSAT…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…