Related papers: Recursive axiomatizations for representable posets
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality and the height of the poset. We explicitly describe…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.
Proof systems for the Relativized Propositional Calculus are defined and compared.
Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type B, we show the existence of basic sets for the matrices of constructible representations. Then we study…
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…
We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…
This paper examines a systematic method to construct a pair of (inter-related) root systems for arbitrary Coxeter groups from a class of non-standard geometric representations. This method can be employed to construct generalizations of…