Related papers: First-Order Stable Model Semantics and First-Order…
We present a study of the notion of coalgebraic simulation introduced by Hughes and Jacobs. Although in their original paper they allow any functorial order in their definition of coalgebraic simulation, for the simulation relations to have…
Logical Neural Networks (LNNs) are a type of architecture which combine a neural network's abilities to learn and systems of formal logic's abilities to perform symbolic reasoning. LLNs provide programmers the ability to implicitly modify…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The…
We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
Notions of asimulation and k-asimulation introduced in [Olkhovikov, 2011] are extended onto the level of predicate logic. We then prove that a first-order formula is equivalent to a standard translation of an intuitionistic predicate…
Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…
Full first order linear logic can be presented as an abstract logic programming language in Miller's system Forum, which yields a sensible operational interpretation in the 'proof search as computation' paradigm. However, Forum still has to…
First-Order Logic (FOL), also called first-order predicate calculus, is a formal language that provides a framework to comprehensively represent a world and its present state, including all of its entities, attributes, and complex…
We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Sigma_1 level of the…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
Existing work on theorem proving for the assertion language of separation logic (SL) either focuses on abstract semantics which are not readily available in most applications of program verification, or on concrete models for which…
The Smodels system implements the stable model semantics for normal logic programs. It handles a subclass of programs which contain no function symbols and are domain-restricted but supports extensions including built-in functions as well…
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.