Related papers: Model theory of second order logic

This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

This survey contains the main results in rational homotopy, from the beginning to the most recent ones. It makes the status of the art, gives a short presentation of some areas where rational homotopy has been used, and contains a lot of…

This article identifies and discusses the theoretical foundations that were considered in the design of the A2RD model. In addition to the points considered, references are made to the studies available and considered in the approach.

We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order;…

Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…

We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new…

The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.

This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…

We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.

We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.

The main focus of this paper is on bisimulation-invariant MSO, and more particularly on giving a novel model-theoretic approach to it. In model theory, a model companion of a theory is a first-order description of the class of models in…

We present a framework for model theoretic forcing in a non-first-order context, and present some applications of this framework to Banach space theory.

Literature involving preferences of artificial agents or human beings often assume their preferences can be represented using a complete transitive binary relation. Much has been written however on different models of preferences. We review…

This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories.…

Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…

The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…

Ordered item response models that are in common use can be divided into three groups, cumulative, sequential and adjacent categories model. The derivation and motivation of the models is typically based on the assumed presence of latent…