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Considering the speed in which humans resolve syntactic ambiguity, and the overwhelming evidence that syntactic ambiguity is resolved through selection of the analysis whose interpretation is the most `sensible', one comes to the conclusion…
In this paper, we discuss Semantic Construction Grammar (SCG), a system developed over the past several years to facilitate translation between natural language and logical representations. Crucially, SCG is designed to support a variety of…
We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…
A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons…
Thirty years ago, I introduced a non-commutative variant of classical linear logic, called "pomset logic", issued from a particular categorical interpretation of linear logic known as coherence spaces. In addition to the usual commutative…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
We introduce (1) a novel parser for Minimalist Grammars (MG), encoded as a system of first-order logic formulae that may be evaluated using an SMT-solver, and (2) a novel procedure for inferring Minimalist Grammars using this parser. The…
To model behavioral and neural correlates of language comprehension in naturalistic environments researchers have turned to broad-coverage tools from natural-language processing and machine learning. Where syntactic structure is explicitly…
Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes…
Categorial type logics, pioneered by Lambek, seek a proof-theoretic understanding of natural language syntax by identifying categories with formulas and derivations with proofs. We typically observe an intuitionistic bias: a structural…
Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP,…
In a recent paper, the author has shown how Interaction Graphs models for linear logic can be used to obtain implicit characterisations of non-deterministic complexity classes. In this paper, we show how this semantic approach to Implicit…
Markov logic uses weighted formulas to compactly encode a probability distribution over possible worlds. Despite the use of logical formulas, Markov logic networks (MLNs) can be difficult to interpret, due to the often counter-intuitive…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras…
We introduce Logic Guided Machine Learning (LGML), a novel approach that symbiotically combines machine learning (ML) and logic solvers with the goal of learning mathematical functions from data. LGML consists of two phases, namely a…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
The model of cognition developed in (Smolensky and Legendre, 2006) seeks to unify two levels of description of the cognitive process: the connectionist and the symbolic. The theory developed brings together these two levels into the…
Logic Programming languages and combinational circuit synthesis tools share a common "combinatorial search over logic formulae" background. This paper attempts to reconnect the two fields with a fresh look at Prolog encodings for the…