Automatic Generation of Proof Tactics for Finite-Valued Logics

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful systems resides in their responsiveness to extensibility of their reasoning capabilities, being designed over rule-based programming languages that allow the user to build her own `programs to construct proofs' - the so-called proof tactics. The present contribution discusses the implementation of an algorithm that generates sound and complete tableau systems for a very inclusive class of sufficiently expressive finite-valued propositional logics, and then illustrates some of the challenges and difficulties related to the algorithmic formation of automated theorem proving tactics for such logics. The procedure on whose implementation we will report is based on a generalized notion of analyticity of proof systems that is intended to guarantee termination of the corresponding automated tactics on what concerns theoremhood in our targeted logics

Towards an efficient prover for the C1 paraconsistent logic

The KE inference system is a tableau method developed by Marco Mondadori which was presented as an improvement, in the computational efficiency sense, over Analytic Tableaux. In the literature, there is no description of a theorem prover based on the KE method for the C1 paraconsistent logic. Paraconsistent logics have several applications, such as in robot control and medicine. These applications could benefit from the existence of such a prover. We present a sound and complete KE system for C1, an informal specification of a strategy for the C1 prover as well as problem families that can be used to evaluate provers for C1. The C1 KE system and the strategy described in this paper will be used to implement a KE based prover for C1, which will be useful for those who study and apply paraconsistent logics.Comment: 16 page

An informational view of classical logic

We present an informational view of classical propositional logic that stems from a kind of informational semantics whereby the meaning of a logical operator is specified solely in terms of the information that is actually possessed by an agent. In this view the inferential power of logical agents is naturally bounded by their limited capability of manipulating \u201cvirtual information\u201d, namely information that is not implicitly contained in the data. Although this informational semantics cannot be expressed by any finitely- valued matrix, it can be expressed by a non-deterministic 3-valued matrix that was first introduced by W.V.O. Quine, but ignored by the logical community. Within the general framework presented in [21] we provide an in-depth discussion of this informational semantics and a detailed analysis of a specific infinite hierarchy of tractable approximations to classical propositional logic that is based on it. This hierarchy can be used to model the inferential power of resource-bounded agents and admits of a uniform proof-theoretical characterization that is half-way between a classical version of Natural Deduction and the method of semantic tableaux

Effective prover for minimal inconsistency logic

In this paper we present an e ective prover for mbC, a minimal inconsistency logic. The mbC logic is a paraconsistent logic of the family of logics of formal inconsistency. Paraconsistent logics have several philosophical motivations as well as many applications in Arti cial Intelligence such as in belief revision, inconsistent knowledge reasoning, and logic programming. We have implemented the KEMS prover for mbC, a theorem prover based on the KE tableau method for mbC. We show here that the proof system on which this prover is based is sound, complete and analytic. To evaluate the KEMS prover for mbC, we devised four families of mbC-valid formulas and we present here the rst benchmark results using these families.IFIP International Conference on Artificial Intelligence in Theory and Practice - Expert SystemsRed de Universidades con Carreras en Informática (RedUNCI

Effective prover for minimal inconsistency logic

In this paper we present an e ective prover for mbC, a minimal inconsistency logic. The mbC logic is a paraconsistent logic of the family of logics of formal inconsistency. Paraconsistent logics have several philosophical motivations as well as many applications in Arti cial Intelligence such as in belief revision, inconsistent knowledge reasoning, and logic programming. We have implemented the KEMS prover for mbC, a theorem prover based on the KE tableau method for mbC. We show here that the proof system on which this prover is based is sound, complete and analytic. To evaluate the KEMS prover for mbC, we devised four families of mbC-valid formulas and we present here the rst benchmark results using these families.IFIP International Conference on Artificial Intelligence in Theory and Practice - Expert SystemsRed de Universidades con Carreras en Informática (RedUNCI

A \textsf{C++} reasoner for the description logic \shdlssx (Extended Version)

We present an ongoing implementation of a \ke\space based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic \dlssx (shortly \shdlssx). The reasoner checks the consistency of \shdlssx-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports \shdlssx-KBs serialized in the OWL/XML format. To the best of our knowledge, this is the first attempt to implement a reasoner for the consistency checking of a description logic represented via a fragment of set theory that can also classify standard OWL ontologies.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1702.03096, arXiv:1804.1122

Informational Semantics, Non-Deterministic Matrices and Feasible Deduction

AbstractWe present a unifying semantic and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic in which the number of nested applications of a single structural rule, representing the classical Principle of Bivalence (classical cut), is bounded above by a fixed natural number. These approximations provide a hierarchy of tractable logical systems that indefinitely converge to classical propositional logic. The operational rules are shared by all approximation systems and are justified by an "informational semantics" whereby the meaning of a logical operator is specified solely in terms of the information that is actually possessed by an agent