Related papers: A decidable subclass of finitary programs
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
The decidability of the reachability problem for finitary PCF has been used as a theoretical basis for fully automated verification tools for functional programs. The reachability problem, however, often becomes undecidable for a slight…
We reflect on programming with complicated effects, recalling an undeservingly forgotten alternative to monadic programming and checking to see how well it can actually work in modern functional languages. We adopt and argue the position of…
Programming by Example (PBE) is the task of inducing computer programs from input-output examples. It can be seen as a type of machine learning where the hypothesis space is the set of legal programs in some programming language. Recent…
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,…
In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to…
Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…
Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling…
We consider the two-variable fragment FO^2[<] of first-order logic over finite words. Numerous characterizations of this class are known. Th\'erien and Wilke have shown that it is decidable whether a given regular language is definable in…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
In this paper we propose an extension of Defeasible Logic to represent and compute three concepts of defeasible permission. In particular, we discuss different types of explicit permissive norms that work as exceptions to opposite…
The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
The paper is organized as a self-contained literate Prolog program that implements elements of an executable finite set theory with focus on combinatorial generation and arithmetic encodings. The complete Prolog code is available at…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets. Francois Fages showed that if a logic program satisfies a certain…
Answer set programming (ASP) is an efficient problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementations in many different fields.…