Related papers: Computation by infinite descent made explicit
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
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…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
We introduce the notion of finitary computable reducibility on equivalence relations on the natural numbers. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular,…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness…
Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible…
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…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
We show how solutions to many recursive arena equations can be computed in a natural way by allowing loops in arenas. We then equip arenas with winning functions and total winning strategies. We present two natural winning conditions…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…