Related papers: On First-Order Model-Based Reasoning
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
We address the problem of semantic querying of relational databases (RDB) modulo knowledge bases using very expressive knowledge representation formalisms, such as full first-order logic or its various fragments. We propose to use a…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…
We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
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…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
Human reasoning involves different strategies, each suited to specific problems. Prior work shows that large language model (LLMs) tend to favor a single reasoning strategy, potentially limiting their effectiveness in diverse reasoning…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
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…
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…
The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…
In this paper, we propose a first-order ontology for generalized stratified order structure. We then classify the models of the theory using model-theoretic techniques. An ontology mapping from this ontology to the core theory of Process…