Related papers: Analytic Tableaux for Simple Type Theory and its F…
We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…
We set out a general methodology for producing tableau systems for propositional logics via a tableau metatheory that provides general and formal notions for different tableau systems that vary by semantics or formulae. Moreover, by dint of…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations…
We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results…
We consider certain decision problems for the free model of the theory of Cartesian monoids. We introduce a model of computation based on the notion of a single stack one-way PDA due to Ginsburg, Greibach and Harrison. This model allows us…
A definable type of a first-order theory is the same as a section (retraction) of the simplicial path space (decalage) of its space of types viewed as a simplicial topological space; as is well-known, in the category of simplicial sets such…
This paper continues the discussion of the representation of ontologies in the first-order logical environment FOLE. According to Gruber, an ontology defines the primitives with which to model the knowledge resources for a community of…
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the…
We identify complete fragments of the Simple Theory of Types with Infinity ($\mathrm{TSTI}$) and Quine's $\mathrm{NF}$ set theory. We show that $\mathrm{TSTI}$ decides every sentence $\phi$ in the language of type theory that is in one of…
Standard Type Theory, STT, tells us that $b^n(a^m)$ is well-formed iff $n=m+1$. However, Linnebo and Rayo (2012) have advocated for the use of Cumulative Type Theory, CTT, which has more relaxed type-restrictions: according to CTT,…
The calculus of Dependent Object Types (DOT) has enabled a more principled and robust implementation of Scala, but its support for type-level computation has proven insufficient. As a remedy, we propose $F^\omega_{..}$, a rigorous…
On the ground of a general theorem concerning the admissibility of the structural rules in sequent calculi with additional atomic rules, we develop a proof theoretic analysis for several extensions of the ${\bf G3[mic]}$ sequent calculi…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
We study the first-order (FO) model checking problem of dense graphs, namely those which have FO interpretations in (or are FO transductions of) some sparse graph classes. We give a structural characterization of the graph classes which are…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…
In this paper we investigate using the methodology of algebraic logic, deep algebraic results to prove three new omitting types theorems for finite variable fragments of first order logic. As a sample, we show that it T is an L_n theory and…
Using Isabelle/HOL, we verify the state-of-the-art decision procedure for multi-level syllogistic with singleton (MLSS for short), which is a quantifier-free fragment of set theory. We formalise its syntax and semantics as well as a sound…