Related papers: A Heuristic Proof Procedure for First-Order Logic
Large language models (LLMs) excel at complex tasks with advances in reasoning capabilities. However, existing reward mechanisms remain tightly coupled to final correctness and pay little attention to the underlying reasoning process:…
We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step…
This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
Ehrenfeucht-Fraisse games are very useful in studying separation and equivalence results in logic. The standard finite Ehrenfeucht-Fraisse game characterizes equivalence in first order logic. The standard Ehrenfeucht-Fraisse game in…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
Heuristics are a central component of deterministic planning, particularly in domain-independent settings where general applicability is prioritized over task-specific tuning. This work revisits that paradigm in light of recent advances in…
Recent advances in Large Language Models have led to remarkable achievements across a variety of Natural Language Processing tasks, making prompt engineering increasingly central to guiding model outputs. While manual methods can be…
In this paper paraconsistent first-order logic LP^{#}_{\omega} with restricted modus ponens rule and infinite hierarchy levels of contradiction is proposed. Corresponding paraconsistent set theory KSth^{#}_{\omega} is discussed.Axiomatical…
We introduce a proof system for Hajek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL, are sound and invertible with respect to any valuation of BL into a suitable…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Goedel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but…
Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations or chain-of-thoughts (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…