Related papers: The Multiverse: Logical Modularity for Proof Assis…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.…
Logic reasoning has been critically needed in problem-solving and decision-making. Although Language Models (LMs) have demonstrated capabilities of handling multiple reasoning tasks (e.g., commonsense reasoning), their ability to reason…
The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we present a framework for the verification in Coq of properties of programs manipulating the…
This work discusses how to build more rational language and multimodal agents and what criteria define rationality in intelligent systems. Rationality is the quality of being guided by reason, characterized by decision-making that aligns…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to…
Causal models are playing an increasingly important role in machine learning, particularly in the realm of explainable AI. We introduce a conceptualisation for generating argumentation frameworks (AFs) from causal models for the purpose of…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…
Multi-adjoint logic programming is a general framework with interesting features, which involves other positive logic programming frameworks such as monotonic and residuated logic programming, generalized annotated logic programs, fuzzy…
The actual existence of collections of universes -- multiverses -- is strongly suggested by leading approaches to quantum cosmology, and has been proposed earlier as an attractive way to explain the apparent fine-tuned character of our…
We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…