Logic and Its Applications: 10th Indian Conference, ICLA 2023, Indore, India, March 3–5, 2023, Proceedings

Description

Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023. Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs. Preface Organization Contents A Note on the Ontology of Mathematics 1 Introduction 2 Continuum and Continuum Hypothesis 3 Inconsistency-Tolerance 4 Concluding Remarks References Boolean Functional Synthesis: From Under the Hood of Solvers 1 Introduction 2 Problem Statement 3 Some Applications 4 Under the Hood of Modern Solvers 4.1 Unique Functional Dependencies 4.2 Unate Variables 4.3 Guess, Check and Repair 4.4 Knowledge Compilation 4.5 Incremental Determinization 4.6 Input Output Separation 5 Conclusion References Labelled Calculi for Lattice-Based Modal Logics 1 Introduction 2 Preliminaries 2.1 Basic Normal Non-distributive Modal Logic, Its Associated ALBA-language, and Some of Its Axiomatic Extensions 2.2 L-algebras, Their Canonical Extensions, and the Algebraic Interpretation of the Extended Language of ALBA 2.3 The Algorithm ALBA 3 The Labelled Calculus A.L and Some of Its Extensions 4 Properties of the Calculus A.L 4.1 Soundness 4.2 Syntactic Completeness 4.3 Conservativity 4.4 Cut Elimination and Subformula Property 5 A.L Is a Proper Labelled Calculus 6 Conclusions A Proper Labelled Calculi References Two Ways to Scare a Gruffalo 1 Introduction 2 Models and Logic 2.1 Updating Kripke Models with Actions 2.2 Logic 2.3 Proof System 3 Agent-Update Actions and Their Logic 3.1 Private Update and Lying 3.2 Forgery with Deception and Without 3.3 Agent-Deletion with Deception and Without 3.4 Private Agent-Addition: +Y for X 3.5 Downgrade and Deceptive Downgrade 3.6 Upgrade and Deceptive Upgrade 4 Some Results for Agent Update Logic 5 Planning 6 Conclusion References Determinacy Axioms and Large Cardinals 1 Introduction 2 Determinacy for Games of Length and Large Cardinals 3 Determinacy for Games Longer Than 4 Strong Models of Determinacy for Games of Length References Big Ideas from Logic for Mathematics and Computing Education 1 Logic in School Mathematics 1.1 Geometric Reasoning 1.2 Propositional Reasoning 1.3 What is Achieved 2 Conceptual Difficulties 3 Big Ideas 4 Reasoning About Algorithms 5 Experiences 5.1 Algebra Tricks 5.2 What are Foundations? 6 Room for Logic References Modal Logic of Generalized Separated Topological Spaces 1 Introduction 2 Preliminaries 3 Generalized Separation Axioms 4 Modal Logic wK4T0n 5 Concluding Remarks References Multiple-Valued Semantics for Metric Temporal Logic 1 Introduction 2 Language and Semantics 3 Normal M-Modal Logics 4 Finite Model Property 5 Concluding Remarks References Segment Transit Function of the Induced Path Function of Graphs and Its First-Order Definability 1 Introduction 2 Preliminaries 3 Segment Function Corresponding to the Induced Path Function 4 Characterisation of Graph Classes Using 5 Conclusion References Fuzzy Free Logic with Dual Domain Semantics 1 Introduction 2 Fuzzy Free Logic with Dual Domain Semantics (FFDS) 2.1 The Role of Similarity 2.2 Representation of Properties and Similarity 2.3 Language of FFDS 2.4 Semantics of FFDS 2.5 Axiom Schema of FFDS 2.6 Deduction Rules 3 Soundness of the System 4 Conclusion References A New Dimension of Imperative Logic 1 Logic of Imperatives - Western 2 Logic of Imperatives - Indian 3 Interpretation of Imperatives - Indian 4 Interpretation of imperatives - Western 5 Attempt to Accommodate All Imperatives in Logic References Quasi-Boolean Based Models in Rough Set Theory: A Case of Covering 1 Introduction 2 Rough Set Models - Relational Approach 3 Rough Set Model - Covering Based Approach 3.1 Basics in a Covering Approximation Space 3.2 g-covering Approximation Space 3.3 Rough Set Model for IqBa2 4 Conclusion and Future Work References Labelled Calculi for the Logics of Rough Concepts 1 Introduction 2 Preliminaries 2.1 Basic Normal Non-distributive Modal Logic and Some of Its Axiomatic Extensions 2.2 Relational Semantics of L-logics 2.3 The Logic of Rough Formal Contexts 3 Relational Labelled Calculi for L-logics 3.1 Labelled Calculus R.L for the Basic L-logic 3.2 Relational Calculi for the Axiomatic Extensions of the Basic L-logic 3.3 The Relational Calculus R.L for the L-logic of Rough Formal Contexts 4 Properties of R.L and R.L 4.1 Soundness 4.2 Syntactic Completeness of the Basic Calculus and Its Axiomatic Extensions 5 Conclusions A Soundness of the Basic Calculus B Syntactic completeness References An Infinity of Intuitionistic Connexive Logics 1 Introduction 2 Intuitionistic Connexive Logics 3 Lattices of "426830A m,n "526930B -Connexive Logics 4 Gentzen Sequent Calculi 5 Concluding Remarks A Proof of Lemma11 B Proof of Lemma14 C Proof of Theorem6 References Relational Semantics for Normal Topological Quasi-Boolean Logic 1 Introduction 2 Normal Topological Quasi-Boolean Logic 3 Involutive Frames and Discrete Duality 4 Some Completeness Results 5 Finite Model Property 6 Concluding Remarks References Author Index