Semantic Relevance

International audienceAbstract A clause C is syntactically relevant in some clause set N , if it occurs in every refutation of N . A clause C is syntactically semi-relevant, if it occurs in some refutation of N . While syntactic relevance coincides with satisfiability (if C is syntactically relevant then $$N\setminus \{C\}$$ N \ { C } is satisfiable), the semantic counterpart for syntactic semi-relevance was not known so far. Using the new notion of a conflict literal we show that for independent clause sets N a clause C is syntactically semi-relevant in the clause set N if and only if it adds to the number of conflict literals in N . A clause set is independent, if no clause out of the clause set is the consequence of different clauses from the clause set. Furthermore, we relate the notion of relevance to that of a minimally unsatisfiable subset (MUS) of some independent clause set N . In propositional logic, a clause C is relevant if it occurs in all MUSes of some clause set N and semi-relevant if it occurs in some MUS. For first-order logic the characterization needs to be refined with respect to ground instances of N and C

A critical examination of Frege's theory of presupposition and contemporary alternatives.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Philosophy.Vita.Bibliography: leaves 385-390.Ph.D

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

Modes of Truth

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics

Iterated Belief Revision Under Resource Constraints: Logic as Geometry

We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the universal memory architecture (UMA)---maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems Z and Z+). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the Sageev-Roller duality between discrete poc sets and discrete median algebras provides a two-way dictionary from inference to geometry, leading to immense savings in computation, at a cost in the quality of representation that can be quantified in terms of topological invariants. Moreover, the same framework naturally enables comparisons between different model spaces, making it possible to analyze the deficiencies of one model space in comparison to others. This paper develops the formalism underlying UMA, analyzes the complexity of maintenance and inference operations in UMA, and presents some learning guarantees for different UMA-based learners. Finally, we present simulation results to illustrate the viability of the approach, and close with a discussion of the strengths, weaknesses, and potential development of UMA-based learners

Modes of Truth

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics

The theory and pedagody of semantic inconsistency in critical reasoning

One aspect of critical reasoning is the analysis and appraisal of claims and arguments. A typical problem, when analysing and appraising arguments, is inconsistent statements. Although several inconsistencies may have deleterious effects on rationality and action, not all of them do. As educators, we also have an obligation to teach this evaluation in a way that does justice to our normal reasoning practices and judgements of inconsistency. Thus, there is a need to determine the acceptable inconsistencies from those that are not, and to impart that information to students. We might ask: What is the best concept of inconsistency for critical reasoning and pedagogy? While the answer might appear obvious to some, the history of philosophy shows that there are many concepts of “inconsistency”, the most common of which comes from classical logic and its reliance on opposing truth-values. The current exemplar of this is the standard truth functional account from propositional logic. Initially, this conception is shown to be problematic, practically, conceptually and pedagogically speaking. Especially challenging from the classical perspective are the concepts of ex contradictione quodlibet and ex falso quodlibet. The concepts may poison the well against any notion of inconsistency, which is not something that should be done unreflectively. Ultimately, the classical account of inconsistency is rejected. In its place, a semantic conception of inconsistency is argued for and demonstrated to handle natural reasoning cases effectively. This novel conception utilises the conceptual antonym theory to explain semantic contrast and gradation, even in the absence of non-canonical antonym pairs. The semantic conception of inconsistency also fits with an interrogative argument model that exploits inconsistency to display semantic contrast in reasons and conclusions. A method for determining substantive inconsistencies follows from this argument model in a 4 straightforward manner. The conceptual fit is then incorporated into the pedagogy of critical reasoning, resulting in a natural approach to reasoning which students can apply to practical matters of everyday life, which include inconsistency. Thus, the best conception of inconsistency for critical reasoning and its pedagogy is the semantic, not the classical.Philosophy Practical and Systematic TheologyD. Phi