Related papers: A Non-Binary Method for Finding Interpolants: Theo…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
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…
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…
Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…
Bilateralism is the position according to which assertion and rejection are conceptually independent speech acts. Logical bilateralism demands that systems of logic provide conditions for assertion and rejection that are not reducible to…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic…
This paper explores goal-directed proof search in first-order multi-modal logic. The key issue is to design a proof system that respects the modularity and locality of assumptions of many modal logics. By forcing ambiguities to be…
While Large language models (LLMs) have the capability to iteratively reflect on their own outputs, recent studies have observed their struggles with knowledge-rich problems without access to external resources. In addition to the…
In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.
Present language understanding methods have demonstrated extraordinary ability of recognizing patterns in texts via machine learning. However, existing methods indiscriminately use the recognized patterns in the testing phase that is…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…
We have been striving to exceed computational complexity, and in the process, we have come to realize the dilemma of classical computing, and in turn we realize that superpositioner may be a way to solve. A superpositioner is a model formed…
Recent research has established complexity results for the problem of deciding the existence of interpolants in logics lacking the Craig Interpolation Property (CIP). The proof techniques developed so far are non-constructive, and no…