Related papers: A Logic of Injectivity
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We investigate purities determined by classes of finitely presented modules including the correspondence between purities for left and right modules. We show some cases where purities determined by matrices of given sizes are different.…
While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…
In this article, we give a family of examples of algebras, showing that for every $n \geq 2$ and $m \geq 0$, there is an algebra displaying a path of n irreducible morphisms between indecomposable modules whose composite lies in the…
This article deals with inductive systems of Toeplitz algebras over arbitrary directed sets. For such a system the family of its connecting injective $*$-homomorphisms is defined by a set of natural numbers satisfying a factorization…
Projectivity and injectivity are fundamental notions in category theory. We consider natural weakenings termed semiprojectivity and semiinjectivity, and study these concepts in different categories. For example, in the category of metric…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally K\"ahler morphism $\pi \colon X \to \Delta$ from $X$ to a complex…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
Let $B\rightarrow A$ be a homomorphism of Hopf algebras and let $C$ be an algebra. We consider the induction from $B$ to $A$ of $C$ in two cases: when $C$ is a $B$-interior algebra and when $C$ is a $B$-module algebra. Our main results…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of…
We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…
A given question can be defined in terms of the set of statements or assertions that answer it. Application of logical inference to these sets of assertions allows one to derive the logic of inquiry among questions. There are interesting…
We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness…