Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming languages and automatically derive associated tools (compilers, debuggers, model checkers, program verifiers). Matching logic does not include a primitive notion of name binding, though binding operators can be represented via an encoding that internalises the graph of a function from bound names to expressions containing bound names. This approach is sufficient…
We present Kaisar, a structured interactive proof language for differential dynamic logic (dL), for safety-critical cyber-physical systems (CPS). The defining feature of Kaisar is *nominal terms*, which simplify CPS proofs by making the frequently needed historical references to past program states first-class. To support nominals, we extend the notion of structured proof with a first-class notion of *structured symbolic execution* of CPS models. We implement Kaisar in the theorem prover KeYmaera X and reproduce an example on the safe operation of a parachute and a case study on ground robot c…
The majority of industrial-strength object-oriented (OO) software is written using nominally-typed OO programming languages. Extant domain-theoretic models of OOP developed to analyze OO type systems miss, however, a crucial feature of these mainstream OO languages: nominality. This paper presents the construction of NOOP as the first domain-theoretic model of OOP that includes full class/type names information found in nominally-typed OOP. Inclusion of nominal information in objects of NOOP and asserting that type inheritance in statically-typed OO programming languages is an inherently nomin…
The Workshops on (Constraint) Logic Programming (WLP) are the annual meeting of the German Society of Logic Programming (Gesellschaft für Logische Programmierung e.V., GLP) and bring together researchers interested in logic programming, constraint programming, answer set programming, and related areas like databases and artificial intelligence (not only from Germany). The International Workshops on Functional and (Constraint) Logic Programming (WFLP) aim at bringing together researchers, students, and practitioners interested in functional programming, logic programming, and their integration.…
CoAlgebraic Logic Programming (CoALP) is a dialect of Logic Programming designed to bring a more precise compile-time and run-time analysis of termination and productivity for recursive and corecursive functions in Logic Programming. Its second goal is to introduce guarded lazy (co)recursion akin to functional theorem provers into logic programming. In this paper, we explain lazy features of CoALP, and compare them with the loop-analysis and eager execution in Coinductive Logic Programming (CoLP). We conclude by outlining the future directions in developing the guarded (co)recursion in logic p…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract d…
The Workshop on Coalgebra, Horn Clause Logic Programming and Types was held on the 28-29 November 2016 in Edinburgh. The workshop marked the end of the EPSRC Grant Coalgebraic Logic Programming for Type Inference, by E. Komendantskaya, Heriot-Watt University and J. Power, University of Bath, UK.
This volume constitutes the pre-proceedings of the 26th International Workshop on Functional and Logic Programming (WFLP 2018). It is formed of those papers selected by the program committee for presentation at the workshop. After discussion at the workshop, the program committee will select a number of papers to be invited for the second round of refereeing and selection for the formal proceedings.
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language") is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic Programming, a fuzzy logic language with explicitly annotated rules) and Bousi~Prolog (which uses a weak unification algorithm and is well suited for flexible query answering). Hence, it properly manages similarity and truth degrees in a single framework combining the expressive benefits of both …
In recent years answer set programming has been extended to deal with multi-valued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy answer set programming solver. A well-known technique for classical ASP consists of translating an ASP program $P$ to a propositional theory whose models exac…
One of the long-standing research problems on logic programming is to treat the cut predicate in a logical, high-level way. We argue that this problem can be solved by adopting linear logic and choice-disjunctive goal formulas of the form $G_0 \add G_1$ where $G_0, G_1$ are goals. These goals have the following intended semantics: $choose$ the true disjunct $G_i$ and execute $G_i$ where $i (= 0\ {\rm or}\ 1)$, while $discarding$ the unchosen disjunct. Note that only one goal can remain alive during execution. These goals thus allow us to specify mutually exclusive tasks in a high-level way.
Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are sought in all areas of logic programming, including but not restricted to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming Techniques. Declarative programming: Declarative program development, Analysis, Type and mode infere…
Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are solicited in all areas of logic programming and related areas, including but not restricted to: - Foundations: Semantics, Formalisms, Answer-Set Programming, Non-monotonic Reasoning, Knowledge Representation. - Declarative Programming: Inference engines, Analysis, Type and mode inference, Partial evaluation, Abstract interpretation, Transformation, Validation, Verification, Debugging, Profiling, Testing, Logic-based domain-specific …
We present a parallel implementation of Coalgebraic Logic Programming (CoALP) in the programming language Go. CoALP was initially introduced to reflect coalgebraic semantics of logic programming, with coalgebraic derivation algorithm featuring both corecursion and parallelism. Here, we discuss how the coalgebraic semantics influenced our parallel implementation of logic programming.
University of Athens（雅典大学）；University of Szeged（塞格德大学）
Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique minimum infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensiona…
Constraint-logic object-oriented programming provides a useful symbiosis between object-oriented programming and constraint-logic search. The ability to use logic variables, constraints, non-deterministic search, and object-oriented programming in an integrated way facilitates the combination of search-related program parts and other business logic in object-oriented applications. With this work we conceptualize array-typed logic variables ("free arrays"), thus completing the set of types that logic variables can assume in constraint-logic object-oriented programming. Free arrays exhibit inter…
Sabanci University（萨班哲大学）；Università di Perugia（佩鲁贾大学）；Universitat Politècnica de València（瓦伦西亚理工大学）；NVIDIA Corporation（英伟达公司）
We are proud to introduce this special issue of Theory and Practice of Logic Programming (TPLP), dedicated to the regular papers accepted for the 35th International Conference on Logic Programming (ICLP). The ICLP meetings started in Marseille in 1982 and since then constitute the main venue for presenting and discussing work in the area of logic programming. Under consideration for acceptance in TPLP.
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 consumed. Because LM integrates both classical and linear logic, LM tends to be more expressive than other logic programming languages. LM programs are naturally concurrent because facts are partitioned by nodes of a graph data structure. Computation is performed at the node level while communication happens between connected nodes. In this paper, we present the s…
This article describes the work presented at the first Logic and Practice of Programming (LPOP) Workshop, which was held in Oxford, UK, on July 18, 2018, in conjunction with the Federated Logic Conference (FLoC) 2018. Its focus is challenges and advances in logic and practice of programming. The workshop was organized around a challenge problem that specifies issues in role-based access control (RBAC), with many participants proposing combined imperative and declarative solutions expressed in the languages of their choice.
This proceedings contains abstracts and position papers for the work presented at the second Logic and Practice of Programming (LPOP) Workshop. The workshop was held online, virtually in place of Chicago, USA, on November 15, 2010, in conjunction with the ACM SIGPLAN Conference on Systems, Programming, Languages, and Applications: Software for Humanity (SPLASH) 2020. The purpose of this workshop is to be a bridge between different areas of computer science that use logic as a practical tool. We take advantage of the common language of formal logic to exchange ideas between these different area…
This volume contains the papers presented at the 23rd Workshop on Logic-based Methods in Programming Environments (WLPE 2013), which was held in Istanbul, Turkey, on August 24 & 25 2013 as a satellite event of the 29th International Conference on Logic Programming, (ICLP 2013).
University of Athens（雅典大学）；University of Victoria（维多利亚大学）
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixed-point of an immediate consequence operator. We also propose an SLD-resolution proof procedure which is proven sound and complete with respect to the minimum model semantics. In other words, we provide a purely extensional theoretical framework f…
This volume constitutes the pre-proceedings of the 28th International Workshop on Functional and Logic Programming (WFLP 2020), organized by the University of Bologna, Italy, as part of Bologna Federated Conference on Programming Languages 2020. The international Workshop on Functional and (constraint) Logic Programming (WFLP) aims at bringing together researchers, students, and practitioners interested in functional programming, logic programming, and their integration. WFLP has a reputation for being a lively and friendly forum, and it is open for presenting and discussing work in progress, …
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a unified language, DA logic, for design and analysis logic, based on the unifying founded semantics and constraint semantics, that support the power and ease of programming with different intended semantics. The key idea is to provide meta-constraints, supports the use of uncertain information in the form of either undefined values or possible combinations of val…
Logic programming such as Prolog is often sequential and slow because each execution step processes only a single, $micro$ connective. To fix this problem, we propose to use $macro$ connectives as the means of improving both readability and performance.
Constraint-logic object-oriented programming, for example using Muli, facilitates the integrated development of business software that occasionally involves finding solutions to constraint-logic problems. The availability of object-oriented features calls for the option to use objects as logic variables as well, as opposed to being limited to primitive type logic variables. The present work contributes a concept for reference type logic variables in constraint-logic object-oriented programming that takes arbitrary class hierarchies of programs written in object-oriented languages into account.…
Adding versatile interactions to goals and queries in logic programming is an essential task. Unfortunately, existing logic languages can take input from the user only via the $read$ construct. We propose to add a new interactive goal to allow for more controlled and more guided participation from the user. We illustrate our idea via \muprolog, an extension of Prolog with bounded choice goals.
The Logic Programming through Prolog has been widely used for supply persistence in many systems that need store knowledge. Some implementations of Prolog Programming Language used for supply persistence have bidirectional interfaces with other programming languages over all with Object Oriented Programing Languages. In present days is missing tools and frameworks for the systems development that use logic predicate persistence in easy and agile form. More specifically an object oriented and logic persistence provider is need in present days that allow the object manipulation in main memory an…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable functions into predicates in order to stay in the logic programming framework. Since amalgamated functional logic languages offer flexible as well as efficient evaluation strategies, we propose an opposite approach in this paper. By mapping logic programs into functional logic programs with a transformation based on inferring functional dependencies, we develop a f…
We present an experimental system strongly inspired by miniKanren, implemented on top of the tactics mechanism of the HOL~Light theorem prover. Our tool is at the same time a mechanism for enabling the logic programming style for reasoning and computing in a theorem prover, and a framework for writing logic programs that produce solutions endowed with a formal proof of correctness.
This paper presents PFLP, a library for probabilistic programming in the functional logic programming language Curry. It demonstrates how the concepts of a functional logic programming language support the implementation of a library for probabilistic programming. In fact, the paradigms of functional logic and probabilistic programming are closely connected. That is, language characteristics from one area exist in the other and vice versa. For example, the concepts of non-deterministic choice and call-time choice as known from functional logic programming are related to and coincide with stoch…
This paper introduces techniques to integrate WordNet into a Fuzzy Logic Programming system. Since WordNet relates words but does not give graded information on the relation between them, we have implemented standard similarity measures and new directives allowing the proximity equations linking two words to be generated with an approximation degree. Proximity equations are the key syntactic structures which, in addition to a weak unification algorithm, make a flexible query-answering process possible in this kind of programming language. This addition widens the scope of Fuzzy Logic Programmi…
The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative semantics, which sees logic programs as formulas and its semantics as models. Here, we define a new operational semantics called TSLD-resolution, which stands for Typed SLD-resolution, where we include a value "wrong", that corresponds to the detection of a type error at run-time. For this we define a new typed unification algorithm. Finally we prove the correctn…
A Proof Theoretic Approach to Failure in Functional Logic Programming
如何从程序中提取负信息是逻辑程序设计中的一个重要问题。在这里，我们解决问题的功能逻辑程序，从证明理论的角度来看。我们工作的出发点是CRWL（Constructor based ReWriting Logic），它是一个成熟的函数逻辑编程理论框架，其基本概念是非严格非确定函数。我们提出了一个证明演算，CRWLF，这是能够推导出否定信息的CRWL程序。特别是，CRWLF能够证明CRWL内的复位有限失败。
This publication is to present a summary of research (referred as Klabs - http://www.kappalabs.org) carried out in author's Ph.D studies on topic of application of Logic Programming as scripting language for virtual character behavior control in First Person Shooter (FPS) games. The research goal is to apply reasoning and knowledge representation techniques to create character behavior, which results in increased players' engagement. An extended abstract / full version of a paper accepted to be presented at the Doctoral Consortium of the 30th International Conference on Logic Programming (ICLP…
