Related papers: Sequential decomposition of propositional logic pr…
A program is a finite piece of data that produces a (possibly infinite) sequence of primitive instructions. From scratch we develop a linear notation for sequential, imperative programs, using a familiar class of primitive instructions and…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
We introduce a relational approach to program synthesis. The key idea is to decompose synthesis tasks into simpler relational synthesis subtasks. Specifically, our representation decomposes a training input-output example into sets of input…
We describe an approach for compiling preferences into logic programs under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
We survey recent generalizations and improvements of the linear programming method that involve semidefinite programming. A general framework using group representations and tools from graph theory is provided.
This research note provides algebraic characterizations of the least model, subsumption, and uniform equivalence of propositional Krom logic programs.
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…
Propositional logic serves as a fundamental cornerstone in mathematical logic. This paper delves into a semiring characterization of propositional logic, employing the Gr\"oebner-Shirshov basis theory to furnish an algebraic framework for…
It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
We describe a mathematical structure that can give extensional denotational semantics to higher-order probabilistic programs. It is not limited to discrete probabilities, and it is compatible with integration in a way the models that have…