Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a combinatorial rather than a logical object. We provide ...

The Collatz problem is reformulated in three ways as a non-arithmetic problem in first-order logic.

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method, and argue that non-deceptiveness i...

The generative conception of grammars relies on the derivation process which, to its turn, depends on a hierarchical representation of syntax. We show in this paper how a fully constraint-based approach, avoiding such restriction, can constitute an alternative to generativity and form the basis of a framework for a model-theoretic conception of grammar.

We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles that embed the essence of Meinong’s philosophy and Grice’s conversational principles into a stratified logic, under an unrestricted interpretation of the qu...

Business modelling methods are popular but, since they operate primarily in the early stages of software lifecycles, most are informal. This paper describes how we have used a conventional formal notation (first order predicate logic) in combination with automated support tools to replicate the key components of an established, informal, business modelling method: IBM’s Business System Developm...

A theory is called κ-categorical, or categorical in power κ, if it has one model up to isomorphism of cardinality κ. Morley’s Categoricity Theorem states that if a theory of first order logic is categorical in some uncountable power κ, then it is categorical in every uncountable power. We provide an elementary exposition of this theorem, by showing that a theory is categorical in some uncountab...

We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of Lω1,ω). Theorem: Let T be any complete first-order theory in a countable language with an atomic model. If the pseudo-minimal types are not dense, then there are 2א1 pairwise non-isomorphic atomic models of T , each of size א1.

A novel approach which employs principles of higher order logic analyses was developed to systematically correlate phylogenetic data with phenotype profiles by identification of phenotype specific patterns of presence of multiple proteins. For example, for most genomes expressing trait A, the presence of protein C presumes the presence of protein B, while for other genomes (not expressing the t...