Related papers: Propositional theories are strongly equivalent to …

We consider prescriptive type systems for logic programs (as in Goedel or Mercury). In such systems, the typing is static, but it guarantees an operational property: if a program is "well-typed", then all derivations starting in a…

A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…

We consider team semantics for propositional logic, continuing our previous work (Yang & V\"a\"an\"anen 2016). In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an…

Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…

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…

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…

Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…

Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

The model theory of a first-order logic called N^4 is introduced. N^4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N^4 is very close to classical logic: N^4 has two truth values;…

This paper treats logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so…

We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…

The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of 'strong equivalence' between logical programs that can be verified in 3-valued Goedel logic, G3,…

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…

In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic…

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…

While there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

Applying logic in the area of conceptual modeling has been investigated widely, yet there has been limited uptake of logic-based conceptual modeling in industry. According to some researchers, another formalization of such tools as EER or…