9 citations · 37 across the 32 of their papers we have counts for
11 papers · 1 filter
On the (Intuitionistic) Logic of Next-Token Prediction
Paul Tarau
We model in intuitionistic implicational logic the key enabler of today's GenerativeAI: the next-token prediction in autoregressive causal neural networks. In our framework, next-t…
A Gaze into the Internal Logic of Graph Neural Networks, with Logic
Paul Tarau
Graph Neural Networks share with Logic Programming several key relational inference mechanisms. The datasets on which they are trained and evaluated can be seen as database facts c…
Abductive Reasoning in Intuitionistic Propositional Logic via Theorem Synthesis
Paul Tarau
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem.…
Deriving Theorems in Implicational Linear Logic, Declaratively
Paul Tarau, Valeria de Paiva
The problem we want to solve is how to generate all theorems of a given size in the implicational fragment of propositional intuitionistic linear logic. We start by filtering for l…
Formula Transformers and Combinatorial Test Generators for Propositional Intuitionistic Theorem Provers
Paul Tarau
We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuition…
Modality Definition Synthesis for Epistemic Intuitionistic Logic via a Theorem Prover
Paul Tarau
We derive a Prolog theorem prover for an Intuitionistic Epistemic Logic by starting from the sequent calculus {\bf G4IP} that we extend with operator definitions providing an embed…
Random generation of closed simply-typed -terms: a synergy between logic programming and Boltzmann samplers
Maciej Bendkowski, Katarzyna Grygiel, Paul Tarau
A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has bee…
Ranking and Unranking of Hereditarily Finite Functions and Permutations
Paul Tarau
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranki…
Executable Set Theory and Arithmetic Encodings in Prolog
Paul Tarau
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic…
Pairing Functions, Boolean Evaluation and Binary Decision Diagrams in Prolog
Paul Tarau
A "pairing function" J associates a unique natural number z to any two natural numbers x,y such that for two "unpairing functions" K and L, the equalities K(J(x,y))=x, L(J(x,y))=y…
A Logic Programming Framework for Combinational Circuit Synthesis
Paul Tarau, Brenda Luderman
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two…