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Constraint Handling Rules is an effective concurrent declarative programming language and a versatile computational logic formalism. CHR programs consist of guarded reactive rules that transform multisets of constraints. One of the main…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
This paper introduces a new type of grammar learning algorithm, inspired by string edit distance (Wagner and Fischer, 1974). The algorithm takes a corpus of flat sentences as input and returns a corpus of labelled, bracketed sentences. The…
Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match…
Process calculi based on logic, such as $\pi$DILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
Recent interpretability work often treats a feature as a single global direction, dictionary atom, or latent coordinate shared across contexts. We argue that this ontology can fail in obstructed representation spaces, where locally coherent…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
We investigate how the sentence choice semantics (SCS) for propositional superposition logic (PLS) developed in \cite{Tz17} could be extended so as to successfully apply to first-order superposition logic(FOLS). There are two options for…
Large language models (LLMs) can explain grammatical rules, yet they often fail to apply those rules when judging sentence acceptability. We present "grammar prompting", an explain-then-process paradigm: a large LLM first produces a concise…
Sparse dictionary learning has been a rapidly growing technique in mechanistic interpretability to attack superposition and extract more human-understandable features from model activations. We ask a further question based on the extracted…
Since the introduction of the CDC 6600 in 1965 and its `scoreboarding' technique processors have not (necessarily) executed instructions in program order. Programmers of high-level code may sequence independent instructions in arbitrary…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
How predictable a word is can be quantified in two ways: using human responses to the cloze task or using probabilities from language models (LMs).When used as predictors of processing effort, LM probabilities outperform probabilities…
We extend classical Propositional Logic (PL) by adding a new primitive binary connective $\varphi|\psi$, intended to represent the "superposition" of sentences $\varphi$ and $\psi$, an operation motivated by the corresponding notion of…
The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…
Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. We collect pairs of naturalistic and synthetic reasoning tasks to…
Manual parallelization of code remains a significant challenge due to the complexities of modern software systems and the widespread adoption of multi-core architectures. This paper introduces OMPar, an AI-driven tool designed to automate…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…