Related papers: Denotational semantics as a foundation for cost re…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
The Automatic Amortized Resource Analysis (AARA) derives program-execution cost bounds using types. To do so, AARA often makes use of cost-free types, which are critical for the composition of types and cost bounds. However, inferring…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
We propose a variant of chain of thought (CoT) prompting called Program Trace Prompting that makes explanations more observable while preserving the power, generality and flexibility of CoT. In our approach, few-shot CoT demonstrations are…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
Large language models (LLMs) enable researchers to analyze text at unprecedented scale and minimal cost. Researchers can now revisit old questions and tackle novel ones with rich data. We provide an econometric framework for realizing this…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…
In this paper, we identify a fragment of second-order logic with restricted quantification that is expressive enough to capture numerous static analysis problems (e.g. safety proving, bug finding, termination and non-termination proving,…
Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
In previous work we describe a novel approach to dependent typing based on a multivalued term language. In this technical report we formalise the runtime, a kind of operational semantics, for that language. We describe a fairly…
Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on…
Understanding of free-format multi-step arithmetic word problems with extraneous information is discussed. A model including a full set of general skills necessary for understanding such problems was developed and computer implemented. The…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…