Related papers: Classical linear logic, cobordisms and categorial …
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
A categorial grammar assigns one of several syntactic categories to each symbol of the alphabet, and the category of a string is then deduced from the categories assigned to its symbols using two simple reduction rules. This paper…
The paper describes a parser for Categorial Grammar which provides fully word by word incremental interpretation. The parser does not require fragments of sentences to form constituents, and thereby avoids problems of spurious ambiguity.…
Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…
We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic…
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
The major concern in the study of categories of logics is to describe condition for preservation, under the a method of combination of logics, of meta-logical properties. Our complementary approach to this field is study the "global"…
Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses the graphical calculus of string diagrams to facilitate reasoning about finite dimensional processes. A significant…
This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in…
A logic family is a bunch of logics that belong together in some way. First-order logic is one of the examples. Logics organized into a structure occurs in abstract model theory, institution theory and in algebraic logic. Logic families…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that explains correctly the…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…