Related papers: A formal system for Euclid's Elements
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Autoformalization involves automatically translating informal math into formal theorems and proofs that are machine-verifiable. Euclidean geometry provides an interesting and controllable domain for studying autoformalization. In this…
We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an…
UCLID5 is a tool for the multi-modal formal modeling, verification, and synthesis of systems. It enables one to tackle verification problems for heterogeneous systems such as combinations of hardware and software, or those that have…
In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a…
The Unified Modeling Language (UML) is rapidly emerging as a de-facto standard for modelling OO systems. Given this role, it is imperative that the UML have a well- defined, fully explored semantics. Such semantics is required in order to…
In this note, we introduce the notion of support graph to define explanations for any model of a logic program. An explanation is an acyclic support graph that, for each true atom in the model, induces a proof in terms of program rules…
Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
We introduce sound and complete labelled sequent calculi for the basic normal non-distributive modal logic L and some of its axiomatic extensions, where the labels are atomic formulas of the first order language of enriched formal contexts,…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
We give a short constructive proof for the existence and uniqueness of the rational normal form of a quadratic matrix.
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…