Related papers: Formalizing Constructive Quantifier Elimination in…
An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal…
In this paper we explore a family of type isomorphisms in System F whose validity corresponds, semantically, to some form of the Yoneda isomorphism from category theory. These isomorphisms hold under theories of equivalence stronger than…
We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…
Lossless compression implementations typically contain two programs, an encoder and a decoder, which are required to be inverse to one another. We observe that a significant class of compression methods, based on asymmetric numeral systems…
We consider a logic with truth values in the unit interval and which uses aggregation functions instead of quantifiers, and we describe a general approach to asymptotic elimination of aggregation functions and, indirectly, of asymptotic…
We propose a categorical framework for linear-time temporal verification of effectful higher-order programs, including probabilistic higher-order programs. Our framework provides a generic denotational reduction -- namely, a denotational…
In this report, we study partial quantifier elimination (PQE) for propositional CNF formulas. PQE is a generalization of quantifier elimination where one can limit the set of clauses taken out of the scope of quantifiers to a small subset…
The Agda Universal Algebra Library (UALib) is a library of types and programs (theorems and proofs) we developed to formalize the foundations of universal algebra in dependent type theory using the Agda programming language and proof…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
Scientific communication still mainly relies on natural language written in scientific papers, which makes the described knowledge very difficult to access with automatic means. We can therefore only make limited use of formal knowledge…
This paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of…
The objective of automata learning is to reconstruct the implementation of a hidden automaton, to which only a teacher has access. The learner can ask certain kinds of queries to the teacher to gain more knowledge about the hidden…
The logic of bunched implications (BI) is a substructural logic that forms the backbone of separation logic, the much studied logic for reasoning about heap-manipulating programs. Although the proof theory and metatheory of BI are…
We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions. This result encompasses Ghilardi-Meloni's and Suzuki's…
In this paper, we focus on the design and verification of timed automata (TA). We introduce a new method for assisting construction and verification of TA models along with a tool implementing the proposed method, i.e., ATAC: Automated…
Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…
Let G be a torsion free hyperbolic group. We prove that the elementary theory of G is decidable and admits an effective quantifier elimination to boolean combination of AE-formulas. The existence of such quantifier elimination was…
If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A…
Classically, any structure for a signature $\Sigma$ may be completed to a model of a desired regular theory $T$ by means of the chase construction or small object argument. Moreover, this exhibits $\mathrm{Mod}(T)$ as weakly reflective in…
In the first part of this paper we present a formalization in Agda of the James construction in homotopy type theory. We include several fragments of code to show what the Agda code looks like, and we explain several techniques that we used…