Related papers: Nested Refinements for Dynamic Languages
The present paper gives a mathematical, in particular, syntax-independent, formulation of intensionality and dynamics of computation in terms of games and strategies. Specifically, we give a game semantics for a higher-order programming…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
Most type systems that support polymorphic functions are based on a version of System-F. We argue that this limits useful programming paradigms for languages with lazy evaluation. We motivate an extension of System-F alleviating this…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
This thesis develops a system for automatically analyzing and improving dynamic programs, such as those that have driven progress in natural language processing and computer science, more generally, for decades. Finding a correct program…
The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
Stable Model Semantics and Well Founded Semantics have been shown to be very useful in several applications of non-monotonic reasoning. However, Stable Models presents a high computational complexity, whereas Well Founded Semantics is easy…
Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
A key challenge when statically typing so-called dynamic languages is the ubiquity of value-based overloading, where a given function can dynamically reflect upon and behave according to the types of its arguments. Thus, to establish basic…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
Deep neural network models represent the state-of-the-art methodologies for natural language processing. Here we build on top of these methodologies to incorporate temporal information and model how to review data changes with time.…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
It is well-known that big-step semantics is not able to distinguish stuck and non-terminating computations. This is a strong limitation as it makes very difficult to reason about properties involving infinite computations, such as type…
This paper provides an in-depth examination of the concept of semantic diffusion as a complementary instrument to large language models (LLMs) for design applications. Conventional LLMs and diffusion models fail to induce a convergent,…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
Recent Large Language Models (LLMs) have significantly advanced natural language processing and automated decision-making. However, these models still encounter difficulties when performing complex reasoning tasks involving logical…
There are two shortages in the current Large Language Models (LLMs) era. The first is short of multilingual models, where most LLMs are English-centric and performance is limited on multilingual reasoning. The second is the place of…