Related papers: A Heuristic Proof Procedure for First-Order Logic
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".…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
Multi-step reasoning instruction, such as chain-of-thought prompting, is widely adopted to explore better language models (LMs) performance. We report on the systematic strategy that LMs employ in such a multi-step reasoning process. Our…
Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…
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…
We study a natural hierarchy in first-order logic, namely the quantifier structure hierarchy, which gives a systematic classification of first-order formulas based on structural quantifier resource. We define a variant of…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for…
We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…
Legal Judgment Prediction (LJP) is a pivotal task in legal AI. Existing semantic-enhanced LJP models integrate judicial precedents and legal knowledge for high performance. But they neglect legal reasoning logic, a critical component of…
Dialogue games are a two-player semantics for a variety of logics, including intuitionistic and classical logic. Dialogues can be viewed as a kind of analytic calculus not unlike tableaux. Can dialogue games be an effective foundation for…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…