Results 1  10
of
122
Temporal Interpretation, Discourse Relations and Common Sense Entailment
, 1993
"... This paper presents a formal account of how to determine the discourse relations between sentences in a text, and the relations between the events they describe. The distinct natural interpretations of texts with similar syntax are explained in terms of defeasible rules. These characterise the ef ..."
Abstract

Cited by 126 (19 self)
 Add to MetaCart
This paper presents a formal account of how to determine the discourse relations between sentences in a text, and the relations between the events they describe. The distinct natural interpretations of texts with similar syntax are explained in terms of defeasible rules. These characterise the effects of causal knowledge and knowledge of language use on interpretation. Patterns of defeasible entailment that are supported by the logic in which the theory is expressed are shown to underly temporal interpretation. 1 The Problem of Temporal Relations An essential part of text interpretation involves calculating the relations between the events described. But sentential syntax and compositional semantics alone don't provide the basis for doing this. The sentences in (1) and (2) have the same syntax, and so using compositional semantics one would predict that the events stand in similar temporal relations. (1) Max stood up. John greeted him. (2) Max fell. John pushed him. But in (1...
The ProofTheory and Semantics of Intuitionistic Modal Logic
, 1994
"... Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpret ..."
Abstract

Cited by 102 (0 self)
 Add to MetaCart
Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary metatheory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are selfjustifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic firstorder logic. It is also established that, in many cases, the natural deduction systems induce wellknown intuitionistic modal logics, previously given by Hilbertstyle axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their
Propositional Lax Logic
, 1997
"... We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verification  ..."
Abstract

Cited by 61 (8 self)
 Add to MetaCart
We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verification  as a logical modality. The resulting logic is unorthodox in several respects. As a modal logic it is special since it features a single modal operator fl that has a flavour both of possibility and of necessity. As for hardware verification it is special since it is an intuitionistic rather than classical logic which so far has been the basis of the great majority of approaches. Finally, its models are unusual since they feature worlds with inconsistent information and furthermore the only frame condition is that the fl frame be a subrelation of the oeframe. In the paper we will provide the motivation for Propositional Lax Logic and present several technical results. We will investigate...
The Effect Of Bounding The Number Of Primitive Propositions And The Depth Of Nesting On The Complexity Of Modal Logic
 Artificial Intelligence
, 1995
"... A wellknown result of Ladner says that the satisfiability problem for K45, KD45, and S5 is NPcomplete. This result implicitly assumes that there are infinitely many primitive propositions in the language; it is easy to see that the satisfiability problem for these logics becomes linear time if the ..."
Abstract

Cited by 58 (4 self)
 Add to MetaCart
A wellknown result of Ladner says that the satisfiability problem for K45, KD45, and S5 is NPcomplete. This result implicitly assumes that there are infinitely many primitive propositions in the language; it is easy to see that the satisfiability problem for these logics becomes linear time if there are only finitely many primitive propositions in the language. By way of contrast, we show that the PSPACEcompletness results of Ladner and Halpern and Moses hold for the modal logics Kn ; Tn ; S4n , n 1, and K45n ; KD45n ; S5n , n 2, even if there is only one primitive proposition in the language. We go on to examine the effect on complexity of bounding the depth of nesting of modal operators. If we restrict to finite nesting, then the satisfiability problem is NPcomplete for all the modal logics considered, but S4. If we then further restrict the language to having only finitely many primitive propositions, the complexity goes down to linear time in all cases. This version...
Fusions of description logics and abstract description systems
 Journal of Artificial Intelligence Research
, 2002
"... Abstract Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to moda ..."
Abstract

Cited by 51 (24 self)
 Add to MetaCart
Abstract Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics.
Alternative Semantics for Unawareness
 Games and Economic Behavior
, 2001
"... Modica and Rustichini [1994] provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information structures. More recently, Modica an ..."
Abstract

Cited by 51 (9 self)
 Add to MetaCart
Modica and Rustichini [1994] provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information structures. More recently, Modica and Rustichini [1999] have provided an approach that allows for nontrivial unawareness in partitional information structures. Here it is shown that their approach can be viewed as a special case of a general approach to unawareness
A Nonstandard Approach to the Logical Omniscience Problem
 Artificial Intelligence
, 1990
"... We introduce a new approach to dealing with the wellknown logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which ..."
Abstract

Cited by 50 (4 self)
 Add to MetaCart
We introduce a new approach to dealing with the wellknown logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit'belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL. 1
On the Decision Problem for TwoVariable FirstOrder Logic
, 1997
"... We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity ..."
Abstract

Cited by 48 (1 self)
 Add to MetaCart
We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO² has the finitemodel property, which means that if an FO²sentence is satisfiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO²sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO²sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO² is NEXPTIMEcomplete.
MultiAgent Only Knowing
 JOURNAL OF LOGIC AND COMPUTATION
, 2001
"... Levesque introduced a notion of "only knowing", with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multiagent case. Although t ..."
Abstract

Cited by 41 (6 self)
 Add to MetaCart
Levesque introduced a notion of "only knowing", with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multiagent case. Although there are a number of similarities in their approaches, there are some significant differences. In this paper, we reexamine the notion of only knowing, going back to first principles. In the process, we simplify Levesque's completeness proof, and point out some problems with the earlier definitions. This leads us to reconsider what the properties of only knowing ought to be. We provide an axiom system that captures our desiderata, and show that it has a semantics that corresponds to it. The axiom system has an added feature of interest: it includes a modal operator for satisfiability, and thus provides a complete axiomatization for satisfiability in the logic K45.