Related papers: Expressiveness and Completeness in Abstraction
Effective field theories (EFTs) are widely considered by physicists to be explanatory and to be the appropriate frameworks for modelling various phenomena at different scales. At the same time, they are known to be approximate, restricted,…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…
Despite recent progress in abstractive summarization, systems still suffer from faithfulness errors. While prior work has proposed models that improve faithfulness, it is unclear whether the improvement comes from an increased level of…
OpenAI's o3-preview reasoning model exceeded human accuracy on the ARC-AGI-1 benchmark, but does that mean state-of-the-art models recognize and reason with the abstractions the benchmark was designed to test? Here we investigate…
The set-theoretical model of Goedel's system T is not fully abstract. We also briefly discuss fully abstract models of system T.
We study the relative succinctness and expressiveness of modal logics, and prove that these relationships can be as complex as any countable partial order. For this, we use two uniform formalisms to define modal operators, and obtain…
Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate…
Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we…
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive. Recently, with the growing diversity of systems to be reasoned about (probabilistic, cyber-physical, etc.), the focus shifted to…
Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting…
Abstraction is the process of extracting the essential features from raw data while ignoring irrelevant details. It is well known that abstraction emerges with depth in neural networks, where deep layers capture abstract characteristics of…
Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
The languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we…
In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted…
We prove completeness, interpolation, decidability and an omitting types theorem for certain multi dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach…
This paper establishes relative expressiveness results for several modal mu-calculi interpreted over timed automata. These mu-calculi combine modalities for expressing passage of (real) time with a general framework for defining formulas…
The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…