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We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal…
We study the algorithmic properties of first-order monomodal logics of frames $\langle \mathbb{N}, \leq \rangle$, $\langle \mathbb{N}, < \rangle$, $\langle \mathbb{Q}, \leq \rangle$, $\langle \mathbb{Q}, < \rangle$, $\langle \mathbb{R},…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
We study navigation with limited information in networks and demonstrate that many real-world networks have a structure which can be described as favoring communication at short distance at the cost of constraining communication at long…
We extend the convergence law for sparse random graphs proven by Lynch to arbitrary relational languages. We consider a finite relational vocabulary $\sigma$ and a first order theory $T$ for $\sigma$ composed of symmetry and…
Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and…
Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a…
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
A graph class $\mathscr{C}$ is called monadically stable if one cannot interpret, in first-order logic, arbitrary large linear orders in colored graphs from $\mathscr{C}$. We prove that the model checking problem for first-order logic is…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
We deal with first-order definability in the embeddability ordering $( \mathcal{D}; \leq)$ of finite directed graphs. A directed graph $G\in \mathcal{D}$ is said to be embeddable into $G' \in \mathcal{D}$ if there exists an injective graph…
We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…