Related papers: Natural Deduction and the Isabelle Proof Assistant
We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one…
We show that explicit pragmatic inference aids in correctly generating and following natural language instructions for complex, sequential tasks. Our pragmatics-enabled models reason about why speakers produce certain instructions, and…
We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error…
Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the…
Negation is a common linguistic phenomenon. Yet language models face challenges with negation in many natural language understanding tasks such as question answering and natural language inference. In this paper, we experiment with seamless…
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
Visual AI systems are vulnerable to natural and synthetic physical corruption in the real-world. Such corruption often arises unexpectedly and alters the model's performance. In recent years, the primary focus has been on adversarial…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…
The number $e$ has rich connections throughout mathematics, and has the honor of being the base of the natural logarithm. However, most students finish secondary school (and even university) without suitably memorable intuition for why…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability…
Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess…
We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), a framework for the verification of cyber-physical systems. We describe the semantic foundations of the framework's formalisation in the…