Charles G. Morgan

This paper concerns the theory of morasses. In the early 1970s Jensen defined -morasses for uncountable regular cardinals $\kappa$ and ordinals $\alpha < \kappa$. In the early 1980s Velleman defined -simplified morasses for all regular cardinals $\kappa$. He showed that there is a -simplified morass if and only if there is -morass. More recently he defined -simplified morasses and Jensen was able to show that if there is a -morass then there is a -simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a -simplified morass then there is a -morass.

We introduce a notion of similarity in a finite row-based semantics for a restricted fragment of first-order predicate logic. Rows encode complete patterns of predicate satisfaction, including projections of polyadic predicates, and weighted configurations assign non-negative weights to rows. Similarity is defined as indiscernibility across rows of positive weight, while degrees of similarity are obtained by measuring the proportion of rows on which two constants agree with respect to all projection predicates. The resulting notion is reflexive and symmetric but not transitive, and is best understood as a measure of structural similarity. Absolute identity is recovered as the limiting case of maximal similarity. The framework is finite and decidable, and provides a simple structural account of graded identity.

This paper introduces a finite row-based semantics for a non-nested fragment of first-order predicate logic. Rows are assignments of signs to monadic predicates, including projections of polyadic relations, and configurations of rows represent admissible individuals. Quantified formulas constrain configurations, while ground atomic formulas impose relational constraints without assigning constants to fixed individuals. On this basis, we develop a non-metric account of counterfactual conditionals. Counterfactuals are evaluated relative to configurations and their revisions: compatible antecedents are handled by restriction, while incompatible antecedents are handled by preserving all constraints consistent with the antecedent. This yields distinct “would” and “might” conditionals and avoids collapse to material implication. The semantics is fully finite and decidable, reducing logical evaluation to operations on a fixed combinatorial structure. The framework provides a simple alternative to both classical model theory and possible-worlds approaches to counterfactuals.

We develop a tabular proof-theoretic framework for an extension of Aristotelean logic in which predicates may be formed by arbitrary truth functions. The framework is based on Venn tables, which generalize traditional diagrammatic methods to languages with finitely many predicates. We present a semantics for the language and establish finite model property, compactness, soundness, and completeness. Within this setting, we give constructive procedures for two problems. For hypothesis generation, we describe a method for constructing sets of sentences that can be consistently added to a background theory to derive a given conclusion. For belief revision, we characterize inconsistency in terms of blocked existential requirements on the Venn table and introduce rejection sets that identify sentences whose removal restores consistency. Minimal rejection sets are obtained by a straightforward minimization procedure, and choice functions determine admissible revisions. The methods are fully mechanical up to the selection of a choice function and apply uniformly to complex predicates. The framework is related to AGM belief revision and kernel contraction, but is formulated at the level of finite belief bases and admits direct tabular computation.

Fuzzy logics are systems of logic with infinitely many truth values. Such logics have been claimed to have an extremely wide range of applications in linguistics, computer technology, psychology, etc. In this note, we canvass the known results concerning infinitely many valued logics; make some suggestions for alterations of the known systems in order to accommodate what modern devotees of fuzzy logic claim to desire; and we prove some theorems to the effect that there can be no fuzzy logic which will do what its advocates want. Finally, we suggest ways to accommodate these desires in finitely many valued logics.