相关论文: Theory Plug-in for Rodin 3.x
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
A large part of the use of knowledge base systems is the interpretation of the output by the end-users and the interaction with these users. Even during the development process visualisations can be a great help to the developer. We created…
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are…
Recent research has shown that smaller language models can acquire substantial reasoning abilities when fine-tuned with reasoning exemplars crafted by a significantly larger teacher model. We explore this paradigm for the financial domain,…
Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover…
Choices in the semantics and the signature of a theory are integral in determining how the theory is used and how challenging it is to reason over it. Our interest in this paper lies in the SMT theory of sequences. Various versions of it…
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently…
When optimizing a thread in a concurrent program (either done manually or by the compiler), it must be guaranteed that the resulting thread is a refinement of the original thread. Most theories of valid optimizations are formulated in terms…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
Large Reasoning Models (LRMs) with long chain-of-thought reasoning have recently achieved remarkable success. Yet, equipping domain-specialized models with such reasoning capabilities, referred to as "Reasoning + X", remains a significant…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
Transformers are widely used in NLP tasks. However, current approaches to leveraging transformers to understand language expose one weak spot: Number understanding. In some scenarios, numbers frequently occur, especially in semi-structured…
This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are…
We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then…
This thesis delves into a fortiori arguments in deductive reasoning, underscoring their relevance in various domains such as law, philosophy, and artificial intelligence. The research is centred on employing GPT-3.5-turbo to automate the…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…