Related papers: Monadic Second-Order Logic of Permutations
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
We study Two-Variable First-Order Logic, FO2, under semantic constraints that model hierarchically structured data. Our first logic extends FO2 with a linear order < and a chain of increasingly coarser equivalence relations E_1, E_2, ... .…
Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison $x<y$ and predicates for $x \equiv i \mod n$ has been investigated by Barrington, Compton,…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In…
According to a theorem of Courcelle monadic second-order logic and guarded second-order logic (where one can also quantify over sets of edges) have the same expressive power over the class of all countable $k$-sparse hypergraphs. In the…
This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…
Verification of properties of first order logic with two variables FO2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having…
Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
We study multimodal logics over universally first-order definable classes of frames. We show that even for bimodal logics, there are universal Horn formulas that define set of frames such that the satisfiability problem is undecidable, even…
In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal')…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…