137 research outputs found
Command injection attacks, continuations, and the Lambek calculus
This paper shows connections between command injection attacks,
continuations, and the Lambek calculus: certain command injections, such as the
tautology attack on SQL, are shown to be a form of control effect that can be
typed using the Lambek calculus, generalizing the double-negation typing of
continuations. Lambek's syntactic calculus is a logic with two implicational
connectives taking their arguments from the left and right, respectively. These
connectives describe how strings interact with their left and right contexts
when building up syntactic structures. The calculus is a form of propositional
logic without structural rules, and so a forerunner of substructural logics
like Linear Logic and Separation Logic.Comment: In Proceedings WoC 2015, arXiv:1606.0583
Comparing and evaluating extended Lambek calculi
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was
innovative in many ways, notably as a precursor of linear logic. But it also
showed that we could treat our grammatical framework as a logic (as opposed to
a logical theory). However, though it was successful in giving at least a basic
treatment of many linguistic phenomena, it was also clear that a slightly more
expressive logical calculus was needed for many other cases. Therefore, many
extensions and variants of the Lambek calculus have been proposed, since the
eighties and up until the present day. As a result, there is now a large class
of calculi, each with its own empirical successes and theoretical results, but
also each with its own logical primitives. This raises the question: how do we
compare and evaluate these different logical formalisms? To answer this
question, I present two unifying frameworks for these extended Lambek calculi.
Both are proof net calculi with graph contraction criteria. The first calculus
is a very general system: you specify the structure of your sequents and it
gives you the connectives and contractions which correspond to it. The calculus
can be extended with structural rules, which translate directly into graph
rewrite rules. The second calculus is first-order (multiplicative
intuitionistic) linear logic, which turns out to have several other,
independently proposed extensions of the Lambek calculus as fragments. I will
illustrate the use of each calculus in building bridges between analyses
proposed in different frameworks, in highlighting differences and in helping to
identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona,
Spain. 201
- …