Related papers: Translating SUMO-K to Higher-Order Set Theory
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice,…
A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems. Although these systems seem superficially the same, they differ in a variety of ways; for example, how they handle a…
To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
Graph translation is very promising research direction and has a wide range of potential real-world applications. Graph is a natural structure for representing relationship and interactions, and its translation can encode the intrinsic…
In the paper, we describe all total orders $\succ$ compatible with addition on additive subsemigroup $S$ of finite dimensional spaces over rational numbers. We provide a necessary and sufficient condition under which a finitely generated…
Hierarchical transition systems provide a popular mathematical structure to represent state-based software applications in which different layers of abstraction are represented by inter-related state machines. The decomposition of high…
Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming…
Previous researches have shown that learning multiple representations for polysemous words can improve the performance of word embeddings on many tasks. However, this leads to another problem. Several vectors of a word may actually point to…
Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
Despite their proficiency in various language tasks, Large Language Models (LLMs) struggle with combinatorial problems like Satisfiability, Traveling Salesman Problem, or even basic arithmetic. We address this gap through a novel trial &…
In this paper, we survey the complexity of distinct methods that allow the programmer to synthesize a sup-interpretation, a function providing an upper- bound on the size of the output values computed by a program. It consists in a static…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
We present an extension of System F with higher-order context-free session types. The mixture of functional types with session types has proven to be a challenge for type equivalence formalization: whereas functional type equivalence is…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…