Functorial semantics as a unifying perspective on logic programming

Logic programming and its variations are widely used for formal reasoning in various areas of Computer Science, most notably Artificial Intelligence. In this paper we develop a systematic and unifying perspective for (ground) classical, probabilistic, weighted logic programs, based on categorical algebra. Our departure point is a formal distinction between the syntax and the semantics of programs, now regarded as separate categories. Then, we are able to characterise the various variants of logic program as different models for the same syntax category, i.e. structure-preserving functors in the spirit of Lawvere’s functorial semantics. As a first consequence of our approach, we showcase a series of semantic constructs for logic programming pictorially as certain string diagrams in the syntax category. Secondly, we describe the correspondence between probabilistic logic programs and Bayesian networks in terms of the associated models. Our analysis reveals that the correspondence can be phrased in purely syntactical terms, without resorting to the probabilistic domain of interpretation

Functorial Semantics as a Unifying Perspective on Logic Programming

Logic programming and its variations are widely used for formal reasoning in various areas of Computer Science, most notably Artificial Intelligence. In this paper we develop a systematic and unifying perspective for (ground) classical, probabilistic, weighted logic programs, based on categorical algebra. Our departure point is a formal distinction between the syntax and the semantics of programs, now regarded as separate categories. Then, we are able to characterise the various variants of logic program as different models for the same syntax category, i.e. structure-preserving functors in the spirit of Lawvere’s functorial semantics. As a first consequence of our approach, we showcase a series of semantic constructs for logic programming pictorially as certain string diagrams in the syntax category. Secondly, we describe the correspondence between probabilistic logic programs and Bayesian networks in terms of the associated models. Our analysis reveals that the correspondence can be phrased in purely syntactical terms, without resorting to the probabilistic domain of interpretation

Functorial semantics as a unifying perspective on logic programming

Logic programming and its variations are widely used for formal reasoning in various areas of Computer Science, most notably Artificial Intelligence. In this paper we develop a systematic and unifying perspective for (ground) classical, probabilistic, weighted logic programs, based on categorical algebra. Our departure point is a formal distinction between the syntax and the semantics of programs, now regarded as separate categories. Then, we are able to characterise the various variants of logic program as different models for the same syntax category, i.e. structure-preserving functors in the spirit of Lawvere’s functorial semantics. As a first consequence of our approach, we showcase a series of semantic constructs for logic programming pictorially as certain string diagrams in the syntax category. Secondly, we describe the correspondence between probabilistic logic programs and Bayesian networks in terms of the associated models. Our analysis reveals that the correspondence can be phrased in purely syntactical terms, without resorting to the probabilistic domain of interpretation

IMPORTANCE OF PYTHON PROGRAMMING LANGUAGE IN MACHINE LEARNING.

Python programming language plays a crucial role in machine learning. Python's syntax is straightforward, making it both beginner-friendly and a friendly environment for those new to machine learning. Its simplicity allows developers to focus on logic and algorithms without spending time on complex syntax. This article discusses the importance of the python programming language in machine learning

A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of defining such sequent calculi for Pure Type Systems (PTS, which were originally presented in natural deduction style) and then organizing their rules for effective proof-search. We introduce the idea of Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the syntax of a permutation-free sequent calculus for propositional logic due to Herbelin, which is strongly related to natural deduction and already well adapted to proof-search. The operational semantics is adapted from Herbelin's and is defined by a system of local rewrite rules as in cut-elimination, using explicit substitutions. We prove confluence for this system. Restricting our attention to PTSC, a type system for the ground terms of this system, we obtain the Subject Reduction property and show that each PTSC is logically equivalent to its corresponding PTS, and the former is strongly normalising iff the latter is. We show how to make the logical rules of PTSC into a syntax-directed system PS for proof-search, by incorporating the conversion rules as in syntax-directed presentations of the PTS rules for type-checking. Finally, we consider how to use the explicitly scoped meta-variables of PTSCalpha to represent partial proof-terms, and use them to analyse interactive proof construction. This sets up a framework PE in which we are able to study proof-search strategies, type inhabitant enumeration and (higher-order) unification