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In this article, we give an unconditional definition of the motivic analogue of the intersection complex, establish its basic properties, and prove its existence in certain cases.
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
Hybrid systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. Legged locomotion, robotic manipulation, and additive manufacturing are representative examples…
This work introduces a canonical structure for a broad class of unconstrained first-order algorithms that admit a Lur'e representation, including systems with relative degree greater than one, e.g., systems with delayed gradient feedback.…
We apply a compositional formal modeling and verification method to an autonomous aircraft taxi system. We provide insights into the modeling approach and we identify several research areas where further development is needed. Specifically,…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of…
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
We introduce CPDL+, a family of expressive logics rooted in Propositional Dynamic Logic (PDL). In terms of expressive power, CPDL+ strictly contains PDL extended with intersection and converse (a.k.a. ICPDL) as well as Conjunctive Queries…
The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational…
We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
In this paper we initiate the study of the computational complexity of learning linear temporal logic (LTL) formulas from examples. We construct approximation algorithms for fragments of LTL and prove hardness results; in particular we…
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…
Modal dependence logic (MDL) was introduced recently by V\"a\"an\"anen. It enhances the basic modal language by an operator =(). For propositional variables p_1,...,p_n the atomic formula =(p_1,...,p_(n-1),p_n) intuitively states that the…
We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends…
In recent work, Kobayashi observed that the acceptance by an alternating tree automaton A of an infinite tree T generated by a higher-order recursion scheme G may be formulated as the typability of the recursion scheme G in an appropriate…